Signature Verification -- ML-DSA-65
pk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
signature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
message: DB8494BA19C4118FB15D0ACF4254FD37483FCF4748FD1844F717CE6F69589E61772CFEFA7F9758653409D4EE5A264B834E60D6BB96499EBEB2B06B0BA874BF31E641394CFAA6A2D30DDB8F045876208D2F51DE15E205E8C91B87ECEB05FF3183271B2649665DD3CC49BFDB998D539DA809305516BBBE9C906021191C5223E525A8FC3616A1765EC3F9C5DB53CC337E039F186ACFEA91148EE2A79CCA3689EDB62AAF28B5D752FDE265EE5280B519726C1CA9803295C674B7EFAFA4D61B306A79E3F6E7A887C2FB535B3B0FB3D9EBC87603EAFEF170C1F1D28E99BB
rho: 6C8414380856CB52D79C4B29139FB1839B8606F5948B9D72A956DCF10116DA9E
t1: [[301, 478, 23, 536, 252, 605, 45, 769, 1012, 360, 347, 1022, 364, 6, 184, 293, 144, 647, 342, 1003, 759, 69, 32, 731, 256, 908, 501, 256, 450, 449, 628, 705, 265, 969, 941, 656, 144, 506, 764, 21, 1019, 318, 279, 66, 629, 121, 197, 382, 285, 548, 523, 918, 181, 38, 307, 895, 57, 421, 71, 68, 491, 110, 721, 307, 450, 48, 566, 531, 922, 420, 727, 1008, 423, 110, 696, 796, 686, 876, 813, 474, 891, 443, 259, 345, 517, 427, 288, 386, 188, 818, 125, 541, 196, 714, 972, 28, 622, 444, 922, 214, 97, 310, 1017, 276, 714, 1007, 88, 332, 767, 75, 714, 598, 705, 115, 402, 233, 23, 597, 373, 895, 18, 497, 160, 876, 526, 379, 837, 686, 430, 918, 667, 781, 511, 323, 670, 706, 39, 895, 231, 442, 773, 94, 295, 953, 106, 45, 280, 23, 979, 962, 256, 325, 182, 579, 23, 788, 37, 241, 502, 921, 104, 51, 656, 847, 265, 607, 475, 410, 818, 333, 225, 319, 267, 286, 619, 720, 596, 599, 832, 891, 569, 844, 275, 307, 459, 451, 257, 560, 468, 795, 542, 225, 717, 574, 802, 773, 196, 946, 730, 370, 140, 120, 372, 917, 851, 360, 391, 777, 564, 410, 400, 304, 949, 578, 20, 766, 333, 770, 576, 931, 608, 644, 38, 338, 164, 53, 76, 782, 738, 704, 0, 471, 309, 264, 432, 62, 472, 482, 521, 159, 428, 468, 462, 965, 53, 963, 771, 232, 526, 179, 580, 541, 277, 975, 506, 680],
[214, 736, 472, 614, 519, 1014, 857, 96, 859, 948, 219, 626, 491, 442, 225, 839, 506, 522, 386, 535, 937, 562, 26, 294, 880, 911, 117, 457, 484, 225, 290, 372, 733, 896, 790, 305, 73, 765, 239, 337, 843, 111, 934, 257, 944, 514, 502, 575, 789, 535, 5, 850, 785, 929, 599, 720, 43, 521, 820, 430, 1004, 971, 241, 618, 119, 259, 277, 321, 928, 905, 440, 458, 69, 896, 682, 938, 71, 71, 241, 963, 78, 652, 814, 978, 115, 303, 224, 202, 461, 908, 810, 87, 633, 621, 553, 364, 505, 440, 779, 49, 343, 633, 960, 647, 754, 589, 162, 357, 628, 118, 506, 753, 685, 280, 989, 882, 581, 140, 539, 261, 836, 182, 142, 30, 54, 547, 418, 476, 526, 744, 482, 360, 319, 681, 331, 584, 365, 689, 325, 993, 586, 458, 87, 671, 264, 16, 959, 773, 990, 315, 55, 712, 839, 170, 900, 298, 223, 901, 49, 48, 664, 273, 584, 872, 430, 878, 601, 476, 249, 148, 892, 240, 714, 839, 34, 475, 539, 867, 733, 33, 511, 350, 654, 544, 783, 126, 53, 443, 212, 776, 474, 321, 242, 662, 610, 402, 741, 339, 842, 99, 158, 488, 721, 681, 609, 392, 575, 360, 368, 812, 693, 311, 477, 217, 1005, 442, 447, 271, 796, 548, 750, 898, 786, 20, 867, 227, 114, 218, 149, 970, 432, 464, 807, 144, 357, 43, 328, 249, 477, 11, 763, 926, 389, 255, 738, 606, 38, 326, 66, 903, 456, 610, 384, 152, 912, 440],
[851, 28, 713, 1014, 396, 711, 240, 613, 695, 576, 682, 407, 152, 542, 981, 584, 373, 98, 820, 58, 206, 788, 263, 300, 44, 505, 632, 633, 207, 282, 395, 743, 384, 666, 248, 427, 422, 937, 231, 858, 943, 79, 223, 154, 360, 293, 640, 724, 125, 966, 818, 749, 329, 46, 907, 816, 456, 395, 293, 480, 675, 353, 621, 277, 1004, 975, 954, 263, 37, 504, 830, 431, 328, 748, 84, 149, 71, 296, 27, 682, 875, 140, 660, 144, 913, 276, 750, 892, 382, 850, 749, 473, 822, 431, 348, 648, 58, 912, 977, 259, 52, 754, 209, 825, 1008, 201, 77, 885, 204, 504, 362, 96, 491, 22, 225, 795, 34, 74, 312, 534, 515, 847, 168, 756, 329, 527, 1001, 316, 960, 481, 701, 276, 350, 403, 939, 188, 642, 1011, 607, 773, 230, 650, 622, 195, 345, 795, 638, 1004, 152, 878, 1012, 882, 991, 42, 580, 459, 292, 274, 753, 966, 633, 844, 326, 181, 576, 774, 947, 538, 997, 255, 280, 957, 741, 206, 87, 107, 955, 984, 351, 249, 381, 478, 757, 551, 531, 983, 432, 709, 189, 259, 914, 915, 606, 396, 19, 241, 352, 632, 675, 285, 86, 287, 921, 324, 15, 256, 589, 242, 532, 806, 197, 19, 243, 949, 631, 673, 226, 293, 538, 661, 1014, 740, 205, 696, 802, 819, 538, 929, 851, 849, 823, 616, 334, 465, 799, 498, 316, 836, 358, 973, 160, 794, 431, 893, 239, 974, 95, 206, 299, 373, 961, 308, 143, 110, 143, 965],
[279, 793, 745, 676, 77, 685, 514, 706, 958, 494, 420, 69, 516, 196, 223, 207, 73, 703, 257, 263, 439, 53, 163, 533, 147, 901, 932, 235, 310, 711, 193, 472, 19, 814, 130, 440, 679, 900, 54, 793, 534, 563, 798, 275, 334, 422, 645, 511, 860, 362, 121, 799, 1019, 517, 709, 503, 407, 896, 441, 677, 821, 976, 958, 688, 794, 133, 404, 810, 840, 559, 407, 877, 1019, 183, 63, 709, 532, 1021, 43, 241, 1001, 866, 212, 37, 29, 1001, 804, 464, 981, 860, 159, 19, 189, 930, 853, 804, 533, 330, 854, 288, 392, 956, 321, 975, 982, 399, 626, 762, 815, 405, 674, 875, 500, 417, 408, 173, 701, 957, 556, 283, 630, 935, 416, 171, 896, 989, 721, 211, 893, 985, 746, 795, 395, 418, 1012, 640, 329, 795, 347, 800, 414, 419, 405, 526, 721, 309, 823, 253, 299, 1022, 173, 609, 14, 362, 572, 703, 533, 661, 224, 160, 726, 348, 11, 686, 613, 852, 878, 681, 971, 23, 616, 44, 919, 384, 471, 206, 1012, 644, 968, 66, 959, 342, 32, 882, 454, 907, 395, 801, 400, 765, 17, 1, 786, 285, 947, 503, 183, 657, 807, 41, 174, 832, 9, 760, 396, 472, 288, 794, 847, 964, 721, 456, 17, 919, 87, 568, 328, 942, 589, 981, 347, 83, 198, 216, 721, 68, 679, 197, 931, 183, 622, 613, 745, 752, 522, 346, 600, 115, 815, 706, 134, 543, 351, 143, 829, 1005, 644, 882, 314, 372, 852, 843, 133, 413, 163, 532],
[227, 108, 171, 768, 678, 657, 951, 21, 664, 529, 706, 647, 772, 216, 143, 653, 529, 7, 368, 565, 316, 569, 244, 332, 373, 936, 574, 952, 130, 706, 711, 262, 547, 270, 673, 670, 804, 732, 388, 464, 164, 107, 318, 220, 262, 969, 504, 937, 58, 387, 145, 908, 780, 159, 269, 872, 780, 915, 285, 394, 735, 729, 767, 486, 559, 936, 682, 326, 815, 451, 63, 494, 156, 944, 658, 759, 917, 980, 9, 108, 189, 856, 189, 266, 726, 133, 171, 599, 1011, 992, 485, 285, 980, 270, 833, 784, 854, 527, 461, 84, 702, 62, 706, 972, 217, 533, 816, 985, 900, 107, 430, 726, 960, 583, 746, 596, 424, 1011, 870, 28, 304, 929, 406, 805, 966, 490, 215, 404, 629, 677, 882, 355, 888, 661, 674, 152, 321, 79, 688, 198, 140, 836, 960, 211, 476, 967, 606, 586, 892, 338, 404, 150, 727, 911, 913, 82, 880, 696, 391, 277, 604, 584, 538, 1013, 851, 637, 269, 154, 255, 738, 836, 651, 855, 39, 567, 213, 751, 749, 559, 320, 725, 330, 542, 549, 395, 40, 742, 325, 489, 475, 147, 951, 574, 1009, 188, 207, 703, 815, 793, 268, 1021, 718, 822, 308, 351, 152, 697, 216, 922, 254, 459, 248, 878, 998, 933, 940, 249, 471, 139, 208, 111, 507, 351, 624, 173, 613, 986, 560, 212, 302, 156, 262, 914, 375, 1006, 656, 822, 254, 767, 314, 646, 787, 920, 580, 746, 640, 16, 126, 266, 765, 32, 349, 579, 986, 851, 139],
[958, 476, 918, 116, 271, 741, 608, 278, 815, 559, 989, 543, 40, 765, 288, 1011, 184, 165, 405, 534, 692, 972, 765, 395, 816, 890, 740, 463, 378, 35, 561, 754, 991, 237, 518, 539, 667, 776, 421, 564, 782, 967, 731, 88, 28, 331, 358, 895, 185, 598, 46, 838, 791, 797, 1002, 694, 909, 766, 502, 376, 690, 583, 42, 989, 452, 131, 220, 184, 846, 492, 670, 720, 994, 359, 23, 872, 820, 328, 532, 985, 40, 162, 353, 75, 468, 647, 63, 790, 440, 1014, 816, 559, 165, 18, 434, 348, 603, 212, 729, 482, 274, 67, 233, 771, 601, 178, 638, 427, 154, 941, 787, 163, 798, 970, 1006, 208, 141, 138, 415, 284, 200, 546, 356, 18, 89, 466, 857, 93, 623, 35, 740, 27, 322, 222, 645, 509, 694, 463, 244, 500, 857, 62, 502, 347, 671, 98, 545, 571, 777, 397, 705, 280, 943, 177, 541, 40, 904, 663, 543, 716, 475, 381, 179, 165, 65, 893, 478, 321, 121, 2, 73, 50, 451, 238, 295, 783, 720, 137, 800, 622, 940, 818, 534, 499, 493, 750, 135, 360, 810, 44, 369, 173, 935, 845, 497, 516, 800, 255, 990, 45, 527, 370, 755, 790, 693, 664, 74, 614, 625, 598, 450, 898, 89, 243, 782, 838, 796, 891, 288, 226, 662, 262, 1005, 70, 745, 105, 589, 422, 801, 541, 780, 790, 319, 516, 730, 155, 336, 904, 930, 189, 896, 1018, 735, 829, 996, 89, 50, 404, 132, 13, 813, 488, 477, 435, 966, 730]]
cTilde: F7789A45A3587330E7FCF70695F7F69688A2B8D0CE54F090214F109F56484F98C3AD1A53A5441C2CA72A3B3191BC046F
z: [[510138, -234579, 48923, -517084, -505489, -32849, -70614, -320501, -393243, -208670, -262951, -341748, -494513, 454109, 197872, -161187, -12678, -129883, -327101, -421292, 176734, 308782, 345430, -209293, 45394, 106105, 83885, -156581, -133650, 416464, 28338, -377603, 176239, 487922, -52926, -198294, -329515, 119777, -349204, 81136, -326211, 413168, -437313, 109273, 54937, -411452, -440516, 451272, 234104, 41683, 492223, 106089, 397756, -144893, 522731, -405558, 329719, -72435, 250842, 452343, -372988, -320202, -449893, 167943, -320126, 480183, 73617, 11034, 187489, -509574, -338324, 308299, 294360, -286339, -53777, -442712, 389006, 73069, -187934, 55300, 496022, 77957, 490811, -262424, -262628, -453747, -10563, -311787, -348685, 224786, 141795, 186931, -419429, -187781, -105249, 322312, 422714, -510374, -29659, 172459, -215372, 71499, -9523, -231670, 286015, -348949, -54139, 9692, -67897, 234558, -149921, 148682, 411066, -236390, 508718, 436675, 363781, 39812, 499455, -203475, 53809, 159076, -367850, -194922, 87715, 81623, 424483, -312139, 427374, 376875, 440328, -510521, -395226, -102743, 505833, 199782, -20019, 226357, -105129, -245243, -338447, -255738, 439992, -150838, 329496, 89685, 355648, -352875, -137697, 205489, -481166, 78186, -56172, -435206, -478049, 492422, -116102, -351761, -4060, 248759, 151096, -58622, -95969, 341827, 186512, 6177, 333507, -145931, -4457, 57781, -319009, -438384, -220602, 203369, 113422, 362436, -355564, -348630, 265215, -114664, -94357, 63515, -410079, -460707, 243912, -446623, 204191, 80152, -138852, -501750, -253561, 295002, 260550, 476412, 320780, -74896, -169127, -295293, 293496, 317182, 110136, 269081, 17075, 348386, 342762, -431674, 16028, -344030, 72244, 74281, 413354, -18472, 297589, 141754, -475726, 48593, 26326, 432042, 491619, 228427, -202151, -250824, -430889, 389835, 410039, -88794, 2242, 19680, -363383, -511455, -348512, 443887, 176221, 449162, -386532, -321225, 242112, -158393, 163554, -62339, -400578, 310248, -209487, -180244, -460428, 165591, -13405, -305343, 472286, 296989, 327673, 515290, -178262, -441707, -491898, -143002],
[-393556, -41414, -86034, -146088, -452845, 80460, -446254, -155562, 24789, 130923, -394796, -133706, -216632, -413849, 228936, 46298, 183574, 188490, -342354, 151561, 456646, -249382, 470510, -39201, 26766, 262524, -140511, 429613, -33721, -99188, -108869, -402782, -63958, -155043, -167569, -495938, -434811, 408309, 86068, -71709, -477711, 61340, 464804, -473444, -299386, 349011, -19338, 25170, -56097, -478527, -309743, 198984, -396948, 315508, 505419, -83597, -212348, 486001, 99381, 286560, 330994, 519733, -348260, -163297, 6711, 14178, 123797, -45892, 508372, 68104, -165666, -49499, 55815, 1110, -75016, -297108, 56195, -367017, 21882, 410535, -390145, 396123, -95524, -461074, -197954, 395938, 447024, 338444, 397359, -197679, 129833, -363617, 398571, 346311, 356570, 491301, -345191, -386834, 370752, -317547, -491923, -487217, 136378, -349789, 259811, 285990, -502970, -312128, -31617, -59697, -506828, 499983, -212157, 199534, -338341, 117554, 158900, -6722, -520819, -278432, 409299, -454240, -307715, -273391, -298310, 38661, 357259, 233133, 360881, 109553, 487177, -146118, 10808, -488621, 505841, -373203, -376880, -457525, -468647, 173940, 261799, -8488, 128854, -157295, 110253, 202198, 365587, 36578, 456911, -399454, 358220, -73290, 409162, -17700, 219038, -219462, -449615, -224460, 187990, -25442, 50583, -301454, -237262, -290256, -86958, 496771, -348124, -235540, 115513, -315876, 182928, 335492, 465414, -193222, -444040, -415636, 507854, 141997, -4578, -346623, -49956, -35891, -164668, 501428, 412222, 134067, 223108, -340972, -245458, 131540, 245921, -312517, -154203, 8626, 180257, -128587, -448245, 513375, 5139, -411084, 476552, 80864, -477103, -125556, -395355, -166681, 265854, 158395, 158426, -131769, 397656, 221591, 265501, 366548, 480691, -159587, 124974, -114991, 116455, -183755, 88627, 318597, 292242, -275992, -487349, 225332, 117168, 383608, 17479, 304312, -375824, -247133, 62155, -191278, -434832, 419359, -167575, -389389, 231834, 198079, -370914, -254308, -15876, 301190, -256563, -486102, 192425, 310544, -222495, 356708, -169683, 330334, 110874, -261476, -392632, 30320],
[-279280, 418861, 298401, 418625, -126935, -409277, 142788, -108303, -360535, 241769, -58860, -305830, 379325, -12804, -223664, -132775, 227835, 9218, 298026, -93530, -156088, -216120, 518394, -257125, 275561, 272555, 182014, 494235, 448934, -234511, -350015, 193833, 385954, 189601, -19616, -461945, 452464, -305971, -382817, -80501, 232788, 23350, -259847, -355245, 240374, -252367, 205191, -128830, 51459, -252135, -256776, -444317, 351993, -283542, -74169, -440821, -369918, -93686, 482198, 450214, 257818, 142343, -281541, -227172, 478364, 328712, 266876, 376290, 249967, -225141, 63518, 396405, -135015, -473607, 463421, 48815, -361475, -169501, 237962, 72034, -456876, 456126, 190359, 95056, 326775, 64043, -331846, 344896, 468825, -307875, 184316, -311405, -377025, 57683, -501521, -214102, -320084, -507349, -367459, 211357, 206794, 445608, -523427, 128534, -321879, -8299, 197065, -139666, -252370, 396128, -174018, 77503, 274389, -292420, -167579, 268053, 405880, 430447, 350236, 387003, 160718, -173311, -504242, 236471, -33159, -19135, 8777, -479993, 438175, 482249, -160835, -192461, 237538, -101028, 227863, -156089, -318393, -479272, -417929, -48819, 521495, -265975, 141432, -372329, -401183, -321250, -328669, -104465, 370202, 307903, -236496, -85599, 430784, 466596, -275865, 344, -274093, -275527, -290443, -179936, -384667, 17520, -88783, 456372, -411593, 85408, -517259, -67173, 450685, -402516, -227683, 14323, -122150, 327185, -151453, 7196, 84022, 437517, 258350, -226106, -330471, 45593, -52758, 223462, 316277, -57182, 337879, 182074, 507880, -381487, 273861, -112655, 301039, 116499, 264505, -143497, -339226, -439780, -82583, 218317, 148382, -446024, 324359, 473437, -441655, -475369, 300250, -296360, 300400, 475912, -135989, -415320, -501465, -113857, 304595, -42931, -194750, -210936, -365760, -194501, -155957, -413185, 158906, -396234, -451238, -433327, 265027, -353646, -27475, 425563, -80624, 204443, -279765, -296935, -235965, 180585, 337442, 150221, -148319, 323512, -351903, 460624, -444651, 235491, 356763, 42091, 298084, 449095, -51469, -472395, -457160, 312172, 43120, -318845, 460911, -56222],
[-257156, -74487, 291534, 424441, 183888, 46458, 29089, -3767, -63785, 64921, -252107, 433098, -179911, 509820, -506424, 435444, 287895, 286497, 391861, 305853, 303174, -338842, -261810, -115984, 85460, 270764, -341018, 416157, -267366, 235789, -21900, 145853, -421314, -29348, -257027, -508169, -507529, -104534, -487575, 421096, -396623, 352609, -438936, -235829, -422000, 261811, 238691, -492506, 387699, -171964, 74373, -311694, 344001, 45196, -164993, -301547, 351797, 98293, 405375, 113627, 94439, -284955, 509760, 195426, -92623, 34512, -157438, -403019, 241127, -5210, 223631, -368470, 354525, -160429, 185597, -194719, -51850, 74252, 267500, -462052, -51369, -188314, 158414, 479502, -413610, -274585, 508847, -471711, -261342, 441317, 126982, -215254, -274290, -273820, -505351, -123142, 173095, -222388, -89369, -158789, -506488, -112038, 442077, 501038, 220906, 274131, -75320, 126291, -220595, 150882, 446550, -453470, -328229, -494305, -505175, 335459, -155159, 470365, -460863, 409070, 344651, 363668, 162225, 45620, -105411, -325582, 239777, 110919, 170772, 388011, 14833, -396566, 127372, -449718, -1730, 394076, 248665, 84591, 30304, -109073, 312762, 16339, -230273, 198410, -506114, 488359, 326081, -337087, 287696, -185378, -501896, 71020, 426976, -483456, 240510, 198335, 111066, 103347, -358524, -157208, 185156, -485028, 118932, 431641, 125040, 341744, -200137, -67268, -303580, -64198, -121086, 391421, -432098, -520773, -294988, -227495, -378929, -303969, 341628, -20897, -122899, -478476, -509467, -436360, 154678, -502165, 82973, -290762, 29358, 471484, -484359, -14796, 216189, 437158, 385562, -191705, 472119, -219177, 16224, 128701, -137177, -120793, -237298, 88912, -6209, 436958, -490472, -57622, 249449, -505454, 398529, -399709, 459452, -332658, 171498, -182167, 131499, 369091, 70523, -131974, -442079, -286054, -27783, 212705, -469648, 116162, 13836, 11541, -361820, 414526, 149262, -119464, -104719, -25477, -427088, 445140, -67763, 295750, 97802, -16601, -516591, 309987, -168357, -32341, -135307, -344317, -175321, 471310, 392834, -425628, 59456, 46162, -192012, -84113, 148647, 270281],
[-127978, 102191, -454009, -19929, 297878, 187874, -908, 142176, -34608, 60524, 240758, 333387, 19770, -172811, 107373, -282138, 488451, 11426, 395629, -452418, -194797, 42115, 178597, 157722, 480553, -469904, -286456, 36620, 192006, -109930, -504099, 486482, -6642, 396355, 254151, 425672, -193518, 117979, 344217, 132326, 322345, -74240, -250041, 442526, -128943, -186102, -319217, 63470, -314231, 99945, -448118, 254935, 245086, 336475, 92141, -436503, -60359, -56538, 216113, 403527, -126361, -337455, -45845, 132175, -368794, -8644, 431518, -329524, -278829, 84608, 438582, 197467, -202046, -464193, -93050, 39300, -506633, 325942, -304696, -158423, -479083, 455843, -57385, -356471, -366085, -301417, 394325, -411175, 454568, 213558, 206250, -448369, -68240, -183496, 29143, 251775, -443241, 22311, 301383, -369631, -189915, 212090, -199330, -102791, 386836, 177426, -65648, -405579, 506290, -20952, 468108, 427968, 393796, 206211, 190272, -225406, 520341, 366486, -285475, 213471, 474161, -409506, -269397, -112929, 211052, 181908, -361025, 444247, 10681, 162934, -241667, -167128, -141130, 223762, 516406, -434278, 316893, 254235, 407426, 316104, 322166, -157734, -103346, -390360, -276123, 82455, -324911, -154473, -320100, 26335, 417556, 142861, -118400, -48019, 324103, -488059, 114867, 453929, -128381, 392897, 131196, -152923, 374831, -491938, 21661, 436097, 253513, -107817, -340750, 420700, -82461, -436666, 348846, -314490, 223414, -310615, -381992, -223278, -37919, 128514, -182512, -378158, 90873, -259460, -361868, 186858, 449831, -47429, 221125, -241025, 271117, -292541, -232991, -418501, 51723, -191387, -186899, -192996, -206332, 283069, -417951, -424648, -446259, -435500, 271780, -374168, -196435, -323363, -100350, -285639, 252868, -56090, -3422, -442807, 238601, 231563, 253894, 169262, -477893, 464489, -504310, 193843, 489456, 284203, -61751, -273756, 227484, -225806, -407028, 91864, 450698, 282705, -179964, 94532, -450037, -164781, -264189, 381880, 5556, 339658, -376702, 335307, -375363, -49693, -412939, 433685, 92078, -179094, 173933, -215752, 394475, -421611, 194412, -213530, -126050, 467755]]
h: [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

Proper number of hints provided. Provided: 32, expected: <=55
||z||: 523427, ||z|| check passed
aHat: [[[7362588, 5894154, 5880011, 8096833, 132283, 2283759, 7503937, 2007765, 6714067, 1163014, 3501190, 2442769, 8314130, 413036, 6424373, 2894874, 1160728, 2574248, 7858974, 2221584, 788444, 1217899, 6574777, 1365724, 8131316, 2407711, 749969, 6116699, 3722572, 4990263, 7895726, 4936703, 4443443, 3083631, 1401460, 6829426, 6635222, 1002550, 6868719, 590467, 3062155, 1034810, 2791300, 6684181, 864545, 4268112, 6668335, 4959758, 6103038, 7923878, 3789931, 5845212, 7743477, 279588, 2220977, 3677481, 6465489, 6272993, 7205613, 4566541, 4730453, 5990791, 2366814, 82511, 2928011, 1927602, 2156905, 6817467, 3985005, 6199611, 4281037, 385889, 8628, 1405045, 4379228, 4571305, 4558323, 6828423, 1861327, 1089384, 8003355, 2192764, 5182493, 7397374, 4412405, 5362547, 1275580, 6720126, 4347740, 1674157, 5130420, 7644083, 238361, 4338101, 5039806, 6496887, 5977108, 8024923, 3538949, 1018072, 4443580, 5642240, 5955981, 5772264, 5672318, 5847198, 4377188, 644312, 83535, 1043146, 7391445, 3104582, 3667978, 4731339, 7243530, 3768184, 4953869, 5393736, 6761022, 3212393, 5728202, 1328754, 4337985, 7470928, 5016408, 6307694, 4589681, 4145735, 5363868, 6646807, 5212200, 5502628, 2695363, 2216489, 2712097, 2058591, 7014228, 3272176, 752420, 1380621, 2346735, 3538273, 3898878, 7293582, 7376394, 2478102, 8029360, 5255727, 240535, 5559974, 3757353, 4635218, 1103238, 293420, 3825591, 1119631, 1378076, 731944, 2652510, 8337704, 5222020, 5366576, 2409169, 8059973, 5839850, 3501388, 7922628, 5421756, 2627560, 5865313, 2040681, 7354278, 4738951, 209133, 4056371, 4604652, 6516621, 3421599, 7053857, 5368637, 3752760, 2846019, 2382761, 5481618, 2348337, 2996413, 2126240, 8255689, 204169, 2247633, 1740745, 7498380, 1256707, 2351219, 5885287, 5113736, 2548338, 7145749, 3461299, 4160225, 5771799, 5799718, 7004055, 4114934, 4684975, 6956176, 5212552, 1920834, 2197509, 5279373, 996767, 8243318, 6434224, 8208305, 71818, 2638264, 7537229, 1662416, 6005920, 7377864, 456812, 2670945, 6816367, 8315745, 1958716, 93034, 744698, 7725220, 5902797, 3691912, 2657976, 3471679, 5882891, 310372, 4202355, 5624133, 3893956, 6965316, 5246078, 5629663, 4805644, 5970337, 2035740, 6463727, 2312018, 1363607, 3713025, 7622047, 3603965, 7773586, 3571800, 627625, 3130715, 549897, 7298176, 8359776],
[1165602, 3634040, 7110348, 6039535, 8209112, 8342684, 3376761, 2760752, 201874, 5788205, 6315920, 5758613, 4180208, 3498018, 4506185, 6197602, 4825715, 1413018, 4001908, 5200822, 2321616, 43264, 357657, 3357947, 5478400, 1625148, 7950715, 241908, 5817357, 6314876, 3963827, 2765806, 7187638, 5098494, 4495365, 4124864, 1563629, 6643348, 2155850, 813048, 5462957, 5416878, 5407763, 685417, 1482758, 2211367, 7400454, 5644271, 599228, 1192002, 3950753, 1943948, 4147278, 7709236, 4455786, 5969957, 4873849, 2497883, 7702897, 1951031, 2746827, 541648, 6820767, 4343169, 7809196, 3075663, 2498997, 7516711, 6073110, 3812366, 6180662, 2140253, 955825, 1183827, 3824805, 961270, 2848570, 553317, 945650, 846350, 7115358, 7684494, 3452277, 2829465, 7560733, 7765663, 8046459, 6122871, 2186559, 1063033, 8249483, 1394306, 664161, 7734307, 4722290, 3791427, 2435952, 263490, 1006165, 3331598, 1364040, 995391, 2074495, 1907554, 2358279, 2270487, 634762, 7962901, 5614697, 5786521, 5116667, 1430717, 7455972, 2533159, 7947550, 7739229, 4927600, 241260, 7369022, 6744571, 6680687, 1961030, 2093028, 4786791, 6246262, 4051533, 3634060, 2403470, 2802259, 3645990, 6976210, 4921899, 5421392, 2002756, 6710071, 2947573, 1575303, 4408913, 1184854, 3248924, 8314261, 5273575, 2035537, 3057717, 4276424, 5822730, 2723413, 7019988, 818534, 2429970, 1355058, 7224104, 2099984, 7006142, 1252024, 1322417, 4242718, 1761064, 2157891, 4952775, 2413792, 4326818, 7109905, 5383105, 6756494, 6255540, 2899390, 3086583, 7685346, 4041101, 5334956, 4513393, 6517963, 4356627, 2904889, 2415412, 7209635, 6858378, 3366617, 2446291, 206235, 1998054, 4488129, 4659437, 1338118, 4922652, 6007451, 5557143, 4798024, 86509, 3799432, 5945739, 1001428, 7172374, 2827278, 7428682, 963842, 7199121, 6413373, 6585976, 4442989, 8150284, 459638, 1681794, 4346128, 7943864, 6962572, 7466591, 3401623, 6306091, 4245753, 5519446, 1599041, 2410812, 1955008, 5812175, 7440355, 253888, 4607519, 700571, 7817367, 5129683, 8046724, 1180791, 5121466, 8184965, 6029940, 3191617, 5335654, 7208397, 7752286, 4052684, 1826096, 1681526, 5923139, 4148306, 4764105, 1496019, 8215829, 7787085, 2322997, 4716898, 7780010, 6832169, 5960634, 644622, 2145941, 7046161, 5644191, 5390778, 1364486, 3472707, 4379141, 897129, 6882711, 5430079],
[505114, 5838411, 458830, 7979075, 5670264, 428930, 2058328, 2485778, 858513, 4171598, 771049, 4557941, 7078960, 246752, 7657596, 7311947, 7436757, 1653825, 4568902, 3837170, 6749455, 5267730, 383035, 3909375, 5270349, 145041, 3920578, 5361952, 4096288, 6984536, 259924, 3272990, 884519, 98442, 2659246, 3976976, 6318032, 7515034, 4097893, 7421103, 6440169, 5112475, 827215, 2064256, 4377010, 3093679, 2450524, 3787473, 5776436, 276928, 3714652, 2110852, 5493568, 6075210, 4651349, 3731505, 726674, 1143540, 6882240, 7156679, 4538267, 4665241, 2801764, 7280180, 252381, 6983846, 682666, 745105, 2200604, 853536, 7165497, 7160843, 3730324, 4436126, 5617625, 5189944, 2914093, 4496979, 3516525, 13047, 2428412, 5364195, 1016854, 498020, 4142253, 2140607, 3152766, 1112431, 1234741, 6955238, 5169676, 4631628, 3054791, 2087732, 2465428, 463256, 7167142, 3603646, 2464664, 7639896, 3371774, 6442849, 8136564, 6870187, 7619253, 5091511, 5544448, 7282816, 2676623, 4346091, 7355838, 5624071, 8357150, 7743875, 3316444, 1125481, 2162453, 5269410, 2538916, 7800595, 6026549, 1027938, 4350245, 6420015, 6184288, 6310221, 513821, 7559827, 3953617, 7806425, 5631665, 8280539, 7310264, 2319526, 3949448, 7788157, 7304291, 4928684, 1680833, 823594, 4935571, 1167600, 3779509, 740800, 4440378, 8349898, 2763210, 4889870, 2000015, 7944716, 6271045, 1226933, 5970183, 5409407, 7578268, 8035409, 287674, 5050922, 5844110, 3363, 611252, 2169335, 4209434, 2939101, 1571908, 4275336, 2598254, 6241832, 1325770, 385487, 4351117, 1453115, 25983, 316062, 5096263, 630583, 4570252, 4936580, 777653, 1704006, 707311, 7275667, 5596671, 5821069, 4340668, 8138438, 1949494, 2708823, 5573315, 3015582, 3160028, 2104984, 2106968, 997833, 7668145, 3397302, 4011508, 8157055, 4272834, 6214778, 2211064, 5927928, 1509789, 2125254, 4311991, 5758295, 2999602, 436929, 7424939, 5140240, 7850182, 8208723, 3265879, 2990560, 3494414, 6411512, 1900577, 459225, 2630952, 6593861, 49107, 5564964, 5578656, 810329, 966231, 475707, 703117, 3318228, 3963650, 7675122, 7329663, 3802392, 5855827, 3823188, 2190891, 5445224, 3779374, 3656226, 685799, 5635990, 2857226, 6878675, 3196110, 1046190, 3346555, 3616861, 4973370, 4549612, 7920465, 6300767, 6214323, 5943331, 3155418, 6850125, 4388611, 8062733],
[4737550, 8048528, 4107210, 984588, 7828055, 3274280, 3026894, 5446031, 1903226, 4956883, 8190333, 4285655, 2638668, 2865996, 4366557, 3105262, 3050745, 4540210, 4219641, 5892592, 709806, 6565870, 4668530, 5135327, 275888, 7605568, 6673552, 1174721, 7568946, 4591818, 1071126, 8224313, 74878, 74221, 2650921, 4930059, 5880414, 4860806, 2147990, 5198647, 4458108, 2010112, 3173104, 1823603, 3789165, 5433558, 3378967, 6728625, 7750219, 7182116, 1083409, 4622439, 2706515, 3724290, 4638369, 3629000, 6883744, 5463586, 4104599, 7196998, 4588331, 7691203, 3385192, 5993936, 3219116, 6254121, 4654236, 1134965, 781900, 6078201, 2502042, 2931972, 1709475, 3753804, 4495032, 6564477, 2889019, 1836204, 4419335, 5745087, 1956861, 3165674, 4437600, 3788057, 1494209, 6957226, 3888012, 2305134, 7808636, 6002347, 703111, 6146887, 1123396, 5867795, 5863886, 6860181, 3344048, 6844232, 2344697, 4691877, 1789836, 5604384, 1562372, 7671115, 6494182, 1077688, 5226722, 2222305, 3448059, 6964631, 735555, 1806530, 5128669, 1247084, 6891051, 3774502, 7071578, 3121229, 1390498, 2776435, 6047796, 1999364, 1255580, 7607344, 7487697, 5815697, 863222, 1565596, 6748431, 1788600, 72186, 7635313, 5640986, 7492486, 3364616, 7606064, 409134, 6373849, 5230143, 7269209, 2543774, 7937739, 6835221, 6297779, 3076839, 8243484, 7723477, 1793471, 8167778, 8014589, 2403828, 5272056, 5922292, 5848470, 8119959, 450362, 308340, 6325036, 2715525, 6139470, 702951, 6830200, 1533969, 3208189, 1386152, 2695572, 57146, 3124851, 1632590, 4710462, 2775192, 3937636, 6035512, 2449625, 2783071, 6480750, 3948025, 263952, 5958995, 726354, 7321928, 114339, 2951138, 501832, 4168598, 5687147, 4092669, 716281, 6468313, 1362399, 417794, 6906556, 556054, 7136725, 52745, 7134021, 1704569, 3708079, 98924, 4655931, 3221713, 7343215, 5560813, 4012560, 4777943, 6446589, 6919466, 270230, 2721190, 366025, 2143534, 7839290, 6596444, 1110038, 6822107, 1065872, 3706207, 3491453, 3803748, 796242, 2519451, 6221889, 1420897, 4848962, 8184104, 8263501, 2413988, 6794431, 4461693, 974563, 7867085, 7222624, 1972281, 836427, 7662464, 3687427, 6341463, 6338951, 2921150, 666362, 2709451, 190938, 950143, 1638819, 6705582, 2585679, 1043943, 1029106, 4998840, 2916442, 1752930, 3870477, 6481668, 7946008, 4607663, 6870304],
[3182745, 7923767, 1881512, 5666672, 3725183, 7462747, 7512841, 3948754, 5560866, 7478113, 6686399, 7110333, 797427, 1413528, 4434905, 7426521, 1283785, 1070493, 1926052, 8278452, 8265172, 1683308, 542918, 7668523, 7927651, 5086113, 4245564, 317320, 5063224, 1953522, 4149499, 2179866, 1171448, 1348595, 2384817, 3328575, 5991176, 5141331, 796992, 8111744, 3228087, 3301218, 5012175, 1234729, 5215828, 1741330, 7922946, 6785795, 7014834, 6806591, 7910423, 7715642, 5790481, 4022203, 516672, 4836282, 2151373, 4058635, 6913047, 4275635, 7705427, 6604590, 7387829, 4974745, 7088812, 726735, 3962405, 8008208, 3429879, 1001561, 7385419, 7303017, 6466025, 6802630, 1311406, 7894483, 801809, 3657355, 2115056, 1344905, 3633466, 7685224, 96567, 264529, 1075988, 471700, 183406, 5781459, 8045067, 1116420, 3171056, 6637936, 5732809, 1887054, 93787, 3230012, 2221408, 6731629, 1491280, 6268918, 8069406, 5352542, 2545514, 7361499, 451578, 7885786, 877656, 4628491, 377192, 6953835, 315440, 4907243, 828374, 2615419, 1854080, 5685022, 2738003, 5161035, 877231, 1098777, 7032050, 2523581, 3054229, 7813041, 1301105, 6898779, 3840160, 2323483, 1844776, 3404360, 7510288, 6357935, 7146518, 6628141, 6328184, 2520575, 5841325, 866922, 7180389, 177690, 1900266, 3452835, 2801045, 565750, 7754166, 1207281, 6471304, 5121119, 1736165, 4541924, 2636272, 1752922, 1904579, 6224522, 1807637, 82904, 3077493, 8006917, 6490757, 5522252, 4050886, 3566680, 6799970, 491862, 1829545, 408681, 5167759, 1959073, 4349577, 5517453, 6466427, 6302192, 2422246, 2450064, 6908661, 8272082, 2438312, 577615, 1999103, 6918755, 332211, 711329, 167323, 3256704, 3837251, 7547988, 2158614, 7326568, 5929825, 794757, 7416099, 7528374, 7899484, 4632900, 39588, 3289222, 1066677, 1527274, 6664095, 6906679, 3396863, 2394333, 8096684, 5608590, 4118079, 586518, 4624671, 674078, 617689, 1932984, 6883298, 1980929, 3092564, 5677999, 5254077, 3137360, 965539, 7824182, 5587505, 8242425, 2839164, 360951, 6365190, 12294, 4257900, 1861151, 8334802, 1955050, 4610407, 3205026, 6050521, 3482675, 4673330, 3462746, 7699439, 5489040, 7570779, 6320951, 5133500, 1169752, 5126912, 1454446, 7050478, 4473394, 7308745, 4509160, 3086393, 7483219, 6966811, 4270475, 3829510, 3489376, 3900039, 1472046, 1058760, 4635091]],
[[4783728, 6971984, 6014887, 8177505, 2661206, 5057619, 7104070, 3267204, 2545438, 7808587, 3806208, 1770766, 2076486, 759003, 7539833, 5957880, 2470481, 7257792, 4742953, 4277194, 6602243, 1059796, 4449907, 8068219, 3526629, 1643952, 6556480, 827697, 3586264, 2296454, 7709521, 3871087, 2601231, 4725657, 3978602, 6732125, 4229320, 2053968, 8041951, 7480195, 8281206, 2895434, 4591112, 7379399, 779364, 5507469, 1000837, 7390737, 1666993, 2419123, 4704287, 3243057, 2378154, 4722433, 353944, 2499271, 5904704, 4714191, 2445013, 2827027, 4037839, 4250606, 6845118, 7338574, 2680409, 3271621, 4144600, 5730330, 6299637, 4456499, 1946830, 7962633, 6358559, 1840663, 661337, 3143481, 6856208, 1699830, 7503606, 503423, 4630460, 152989, 5237847, 1852456, 6345160, 818405, 3829701, 23091, 4606903, 783136, 1293595, 6016578, 5807955, 5188939, 5040811, 4049759, 6672616, 4135481, 771424, 4304911, 3339854, 2623875, 1065712, 2875069, 5038555, 2139921, 1368674, 1012534, 1936027, 7272741, 7757387, 4745078, 3661691, 1153798, 1255846, 199994, 1731000, 7662338, 3467728, 5538529, 2194099, 1523320, 5721876, 6925561, 2897407, 5464133, 1065994, 4422408, 5924958, 3441380, 2933156, 850645, 2104296, 6790780, 6426416, 7457680, 7263847, 6124308, 7207235, 8156450, 960128, 5440223, 8154437, 528374, 7583538, 1116435, 6455056, 2760370, 7118778, 1668287, 8090940, 5227125, 4035129, 39516, 3467642, 7472954, 5705942, 2431326, 2631238, 7663266, 563127, 6309747, 5962833, 7973041, 6713059, 1486236, 7200264, 4726754, 4356790, 1700066, 4037329, 5613675, 5401752, 7917892, 3807897, 3206110, 2577303, 2406821, 4512060, 6574960, 96202, 2439024, 210204, 924092, 6263422, 7741747, 4336261, 603309, 1378288, 994890, 546283, 7232013, 5160810, 1430806, 6877074, 6483400, 111382, 4582588, 1773061, 5139852, 4690217, 7689478, 719824, 7076728, 6832204, 8326250, 857254, 5440343, 2746930, 6003197, 5905397, 5111132, 6264746, 3532368, 5919685, 2442829, 6063805, 368540, 8273404, 2175101, 2550107, 6515260, 7028186, 4199062, 7775558, 5884433, 1631362, 2852704, 4100370, 6890550, 1329759, 8008976, 4332620, 6850824, 8324088, 4462596, 1489470, 5336156, 6394613, 2701408, 2903586, 3809008, 333561, 6178734, 5968284, 1644749, 4620162, 1735123, 551435, 5368725, 5238528, 6456315, 4157935, 1173210, 665836, 5654516],
[8066863, 2276547, 6953891, 1462440, 1176768, 1864632, 2710075, 5604281, 2414955, 6704923, 6283663, 639890, 2039091, 4836437, 5210445, 3247845, 6357339, 1958002, 1255963, 1428875, 2984969, 3889466, 6545848, 4486978, 3679093, 7966850, 1439790, 1277904, 3514871, 3145422, 6610604, 6005866, 3156548, 3352067, 4849802, 4988199, 4784287, 5210118, 2020445, 4169917, 1534423, 7100134, 3318134, 5572433, 7518875, 7198171, 2956025, 3171352, 1241811, 2463028, 3136555, 314147, 1805312, 770262, 1806058, 1398905, 708495, 5610281, 4607891, 2953617, 6605103, 5923007, 8038834, 6563577, 4189426, 325266, 8004516, 3649422, 875634, 4463363, 4581655, 8291003, 6045720, 1404232, 1398626, 5310796, 3879650, 2730511, 7226217, 7237437, 7890020, 5175883, 2383216, 5258581, 7548550, 7944568, 8058776, 1966785, 2059705, 8002221, 6688122, 5546498, 7386599, 5543666, 8166202, 634868, 7785138, 5112402, 4391601, 1405198, 3876236, 700375, 774524, 1067817, 3530973, 7103543, 1658058, 7099410, 3876423, 5221750, 2506199, 1724209, 2505794, 3098281, 3698308, 6709122, 8358058, 1385435, 7997912, 8253954, 2920582, 4834713, 6910866, 2306372, 1793155, 7657132, 5049787, 6595121, 3127920, 5591306, 2295253, 5963191, 73680, 3367601, 4053080, 4681502, 7238248, 562430, 4492708, 3607751, 8081555, 5924787, 4950987, 11133, 5363299, 6000270, 6084419, 2714066, 4947097, 164583, 4554139, 8268073, 107772, 5060501, 1275028, 6853258, 4992988, 3350803, 1354897, 6790678, 3139078, 1803038, 5791372, 6623993, 5723158, 3833357, 6459385, 3472174, 2658743, 1093908, 496510, 6388363, 4438387, 6808811, 6472602, 4250950, 1210704, 473341, 990, 4054888, 5717684, 7198170, 1266928, 8059271, 7621431, 1386190, 189584, 1723579, 7635318, 2899180, 260145, 7512010, 1228060, 6001604, 285320, 1334911, 6642978, 1488782, 2552255, 7007241, 3169970, 7348415, 8042986, 6565085, 1293318, 3652276, 2853254, 5192005, 5855669, 4877132, 2615501, 3590133, 2666689, 8148427, 4477653, 127761, 8318770, 1015078, 3768226, 2872895, 5412207, 7111904, 2186685, 7252906, 1955024, 7155630, 1064021, 6217860, 4795666, 6325131, 1605563, 7661337, 764032, 7809716, 4454657, 2572843, 601248, 4524304, 4625812, 2128539, 7750618, 4626730, 1457655, 2810869, 2557993, 4701640, 5409177, 3199315, 6993950, 736152, 1566925, 2974952, 2932134, 753397, 1063094, 2739865],
[6069280, 786561, 5788053, 7004517, 5662557, 6086849, 5955012, 6661186, 4502014, 6473239, 6286892, 7779376, 3960194, 5199936, 5904044, 3537710, 6432962, 7310589, 2630838, 6895247, 867362, 7735717, 3243253, 1043486, 5029787, 6048398, 6849665, 1503762, 5282307, 2131544, 5988162, 6409504, 5291448, 5925297, 6789632, 954809, 1203466, 4849304, 7822917, 471221, 4834366, 7157450, 6259952, 7654366, 430249, 2204218, 8005943, 5964295, 3259679, 4184293, 2663704, 3904292, 7661201, 6897985, 2044288, 8020374, 4594341, 3392810, 1160388, 5795120, 3554426, 4788605, 5800154, 5862918, 4672815, 7452081, 2218410, 5849841, 2197862, 2132099, 6402181, 8374792, 2125942, 921718, 4165551, 8260450, 7796138, 796494, 2886414, 5321119, 4947345, 3236877, 6951953, 6526592, 1628982, 6262455, 2660342, 7346294, 8229148, 6408207, 6282327, 4081341, 8072854, 5375475, 3615723, 5189720, 7467751, 4107131, 1373551, 5614974, 1914531, 6283994, 297571, 4145939, 7401335, 99382, 2214250, 1240172, 4665635, 783655, 7194557, 3989406, 2787997, 1351695, 5266414, 5529245, 5509100, 5094490, 18513, 4629590, 2975864, 4277507, 6727672, 4032433, 7425174, 2685773, 4580873, 2305987, 3801267, 5461311, 1286936, 887206, 4667145, 5849405, 3898691, 75545, 8152764, 7039378, 6765387, 2385854, 2354367, 3159157, 3957469, 1137864, 1644241, 2531833, 3795721, 5778535, 7174456, 363838, 3130965, 4897176, 1535548, 6912009, 3363853, 1977335, 6497406, 5744455, 1828820, 6428542, 3601627, 2055614, 5604306, 4380000, 8258168, 25927, 7036092, 6507512, 2017607, 358102, 5434520, 3438661, 113207, 6073558, 6639252, 4912358, 7591987, 113731, 4703841, 3520752, 5768651, 7245068, 3843634, 528159, 4613596, 5114216, 3970761, 6394271, 1340462, 5187874, 2379454, 1797350, 1236708, 2448333, 7898900, 2276396, 4830019, 5117577, 860621, 4367704, 2524593, 5376756, 3500069, 1565198, 3348738, 2240329, 5081492, 1979726, 5590062, 8046913, 1670529, 584010, 127627, 5686031, 5440992, 5305550, 4014619, 6275190, 5341203, 6330134, 554771, 4177209, 2776280, 5563010, 4266615, 7284994, 3612073, 1981711, 7714091, 5178552, 6367281, 8134955, 3320308, 5043133, 3278310, 2943552, 6868195, 523399, 4054288, 5040244, 7036937, 7942539, 1977036, 5206411, 8292922, 7705689, 4654827, 5197558, 4973709, 2810963, 7244980, 6707947, 7041430, 1906648, 6566226, 3336865],
[5498961, 3744343, 1744591, 5771093, 1864086, 4169853, 5658067, 4505424, 8150478, 7052887, 7870657, 1455412, 8302721, 7510991, 6598293, 2502409, 1335072, 7513612, 4113743, 7983594, 6490596, 3082834, 6248491, 2816095, 5491352, 6351453, 3296646, 7066756, 4723574, 4757057, 2113200, 5156556, 7460681, 6526525, 3419436, 6777718, 6280905, 5940362, 1094782, 5222245, 7930128, 3012655, 6716714, 6599948, 1583851, 3724142, 2818617, 2850875, 4138492, 8027402, 1516295, 2512587, 3812883, 8218814, 8162204, 5342183, 6750511, 4696407, 6803811, 1988193, 6091411, 7837713, 211996, 3448033, 1374581, 976456, 2812510, 1908666, 553685, 2500778, 817995, 1068761, 6448402, 6380704, 8275844, 3864181, 4302496, 6281736, 6763764, 5508602, 264175, 5574015, 5532235, 7389155, 2748919, 107113, 4663132, 6341737, 6870072, 5019670, 2096477, 3078101, 7832196, 8212188, 6002403, 3961224, 1022779, 3006576, 1456670, 807086, 4074388, 329339, 320394, 3570120, 700366, 20195, 3039428, 2769464, 5951510, 6652555, 3042228, 6138697, 3578518, 4472499, 1534404, 2329442, 7208779, 7899268, 8104804, 2483795, 126283, 4975627, 684731, 4440872, 7127495, 33891, 3289351, 655367, 6101208, 206382, 6542372, 5039864, 4823641, 4274797, 2726829, 663536, 7979752, 1555695, 6783797, 1229642, 7519661, 1286734, 2195679, 3117595, 4168892, 6606401, 1061616, 7993894, 869368, 903121, 2991582, 5284940, 6716780, 6641056, 5780271, 2915600, 1839726, 3001351, 4647152, 2946995, 6677256, 1172372, 6765190, 4063711, 7901806, 6386293, 8294540, 6018028, 1247505, 3323246, 8367651, 3268039, 4310569, 2209106, 1733101, 756094, 8028059, 6778338, 6874701, 5488160, 8300304, 2770662, 2311524, 6479013, 4057369, 4642291, 4362855, 7828383, 3687462, 4062397, 6279028, 5364579, 2024472, 3751830, 2711820, 3441194, 6676558, 6812744, 7244993, 209736, 6694137, 3154568, 3435127, 6042054, 1194914, 2951767, 403232, 5587109, 33729, 2708887, 1030025, 8132680, 2646203, 3914926, 836118, 910415, 1821453, 7722119, 6593151, 1205785, 7922844, 5807142, 4283310, 7294327, 1829714, 50252, 1990379, 5640297, 4490746, 4368218, 3251255, 1662411, 3745168, 3500747, 8336978, 5128531, 7320958, 7862469, 4072320, 5691883, 2571366, 3219349, 1510569, 2516773, 5940350, 3387660, 6337468, 6934862, 312194, 828437, 791029, 2742082, 1546571, 5373646, 6816652, 6956156],
[2706883, 6107658, 2033281, 149036, 7821344, 7618267, 686404, 3122621, 3424931, 8027036, 3253496, 4006038, 5827876, 2757145, 2872066, 3593383, 709073, 4114020, 5456743, 6845074, 3783977, 6261953, 7970062, 4667178, 8136437, 5750337, 4656847, 6952418, 2587384, 6887713, 7810529, 1780929, 753606, 2275676, 612064, 6448104, 808719, 801756, 2829692, 7711220, 1621088, 5280589, 5208048, 6393153, 2166081, 883875, 2952260, 7639185, 3355900, 6046584, 3780765, 3564901, 2865078, 303996, 1271372, 4155238, 7585920, 4988568, 798245, 7457732, 3762200, 1400054, 7181915, 523096, 1931365, 1351934, 1737272, 865423, 3172989, 6053719, 7636159, 467009, 4509368, 6447320, 1550112, 5947812, 499992, 692865, 4783736, 3650377, 5519076, 5961849, 358983, 7701352, 797875, 1095094, 3352836, 6015037, 7100354, 3647501, 665289, 4871147, 3042964, 3079407, 1312918, 475735, 6751692, 1882853, 7471407, 593463, 11529, 8074676, 4723326, 6864326, 6013734, 6886115, 8056384, 4349000, 6693745, 3658231, 4727183, 1971070, 792094, 733930, 4348085, 4274492, 316772, 6716258, 6008478, 5862368, 7049821, 5308795, 377484, 5088101, 7636168, 7977524, 7301851, 3156726, 5177329, 2376995, 6419290, 3736612, 7377811, 1306488, 3038888, 4000595, 2855928, 4837253, 4395901, 4576679, 7217788, 6185416, 1001037, 5191043, 3798707, 4149318, 364114, 5980282, 4587427, 3182283, 5645971, 5140737, 4236253, 2139408, 8186791, 5299901, 5312470, 8129822, 5039512, 6575348, 6478803, 6403735, 4002444, 1936281, 5000116, 6164144, 5136625, 7688293, 3440341, 2121264, 3082570, 3421380, 5767638, 6039803, 5869953, 7633856, 5134523, 1968935, 3550880, 7743494, 5236382, 7963736, 538658, 2280489, 2013995, 3077635, 4470065, 285895, 7145945, 8326914, 4326691, 690634, 813715, 5964350, 2949462, 2680371, 2410776, 4746615, 1998581, 5688363, 2363801, 1221648, 2275376, 356199, 857919, 467255, 5163249, 7059089, 576882, 2054238, 511790, 6716965, 6085599, 1217785, 2654120, 2123398, 2388468, 4442586, 6724623, 8134692, 5922416, 243561, 3617046, 2128155, 5505463, 4605385, 8074696, 5203530, 4218433, 2923506, 5188224, 3391883, 115376, 4208181, 1542787, 5187153, 6897608, 417467, 7675178, 5615279, 3425487, 6183386, 6412622, 3607594, 7309397, 6388238, 6805714, 3802317, 6495527, 2776801, 5618297, 7142175, 2039870, 7099895, 98307, 3001133]],
[[6330270, 1454956, 423737, 2159708, 1513591, 7712820, 115013, 5887469, 7164689, 3696178, 3506877, 2991733, 7361799, 3734448, 3001686, 552496, 4833882, 5442740, 3186992, 2546018, 3145068, 1456267, 3641653, 4939672, 2437722, 4892978, 7660632, 3404679, 3831172, 5633959, 4637762, 6548006, 6404029, 5138119, 1325226, 1743657, 5530757, 1548832, 3889476, 7964715, 1939371, 6307460, 2189375, 324282, 5822982, 5586623, 5720658, 7195023, 5866904, 4218349, 4549351, 2999240, 5235855, 3489149, 1408098, 4258620, 5301432, 2741642, 3654318, 4047127, 7720661, 4669693, 361599, 4426208, 5187429, 4952014, 3466344, 7144652, 8359724, 1624306, 4807431, 5234298, 1347029, 2531667, 8106340, 1956221, 4789762, 7496255, 7429973, 234768, 1472055, 1355311, 4997676, 5045709, 908721, 6825370, 4642962, 294904, 6254821, 5917487, 6000892, 2347302, 6904351, 641935, 4308009, 4449497, 6411961, 5002678, 8083598, 5077603, 3872456, 1225553, 7013437, 4638647, 3400976, 5650904, 305831, 4664881, 4290336, 90854, 158438, 876490, 2019619, 2501688, 909885, 1174293, 5979252, 7918656, 2240271, 3486929, 7005313, 2080094, 8313834, 7652267, 216296, 6093751, 2249792, 2176829, 7091446, 8087299, 3970149, 5606280, 1935193, 4466000, 6319863, 2903164, 1099999, 5289087, 6008611, 1341323, 4574467, 3698977, 6779774, 139285, 7075654, 2657246, 168183, 8096963, 5921968, 5559722, 2976993, 6413315, 7304274, 3245566, 1563612, 4510037, 1115062, 7623236, 4566826, 4406596, 5688285, 3420670, 7675720, 4912627, 7553466, 8284383, 3187125, 5780671, 6192043, 195955, 7542069, 2810170, 406156, 785539, 3673950, 1804554, 3016856, 7492345, 7336667, 2860266, 1126645, 5167401, 4448004, 6073815, 3561815, 2695219, 4958808, 2687906, 7488828, 2685417, 1336244, 6869406, 3120405, 3695941, 5604386, 6330750, 831509, 25129, 6871162, 5861696, 152639, 2359904, 4722231, 7073822, 8308080, 4967281, 5766956, 5240112, 3153127, 6616375, 1026933, 3708584, 2358726, 4465843, 1652766, 1096144, 4531127, 4429608, 6375569, 661834, 4918162, 1282278, 2461399, 6192681, 1939023, 5458632, 2632001, 3213576, 1034747, 1547586, 6460208, 6815552, 7071815, 1920284, 7359009, 1805220, 5795512, 3119817, 5260222, 798702, 5058639, 4104107, 3428298, 1875929, 4235280, 6510990, 7413056, 6698208, 4122961, 5356759, 4118102, 1537891, 6915895, 1690716, 7979033, 6968560],
[7778909, 2376505, 5705894, 7001665, 7006783, 3119948, 7174790, 3324582, 4879255, 2202767, 3223028, 3489505, 1002176, 802077, 987670, 8334799, 7671516, 1219791, 4902528, 7323348, 1408958, 8188387, 2694154, 6539988, 6877294, 987408, 7749589, 8117883, 3187316, 7247024, 7949907, 5066592, 4464910, 4039277, 6654077, 8355179, 4486096, 2573916, 1840967, 7879578, 7336711, 4887639, 1028949, 4553191, 417631, 4345900, 1474218, 8073757, 1065141, 3102695, 1238196, 6898487, 1286262, 7510350, 65158, 3485092, 2265654, 247118, 5459601, 4851987, 1923012, 8254284, 1736083, 392521, 1112755, 744483, 4433242, 3594617, 5950574, 1476868, 2905011, 5369434, 4323951, 1054651, 5022564, 2735151, 2473985, 8028893, 713727, 7661374, 7190702, 1511366, 7302453, 5915234, 7156667, 5524142, 5730767, 8164864, 4075995, 5937771, 8086714, 6277311, 6873804, 4717641, 3450221, 1101239, 6311607, 5437737, 1690483, 7446255, 7969006, 301218, 2534440, 7544895, 5450227, 5190944, 179586, 4976218, 6495715, 8194838, 3089964, 6251122, 2602138, 7870696, 432603, 5413960, 2382594, 1839889, 6628828, 4789381, 5421227, 6032337, 2660524, 3725236, 2375595, 5342963, 6521205, 4213417, 127186, 2786044, 1087252, 7334616, 7556590, 1969610, 2263517, 3983278, 6974102, 8101879, 1006484, 1624818, 304226, 6189820, 2594714, 4055729, 4082174, 1361946, 1073827, 7194312, 4055353, 7017060, 401660, 4980368, 225508, 1306914, 2052827, 5120555, 1981558, 2600708, 1507442, 329580, 6497387, 4717951, 3984310, 7735049, 6846575, 3205084, 8216244, 1404151, 7467268, 2807166, 4926364, 8002996, 558406, 5302746, 5815973, 4147201, 3938592, 4937725, 4803551, 3011727, 3016473, 3271680, 5659332, 2463357, 3468841, 1749698, 2471092, 7144971, 6853372, 5237373, 3246937, 5183478, 24281, 8304938, 7954491, 845176, 94984, 3175923, 4768148, 3926602, 3569357, 7750878, 6064424, 5417549, 6455730, 2846210, 2299373, 7714729, 3515480, 7849802, 6254766, 3362353, 89459, 5677227, 1734621, 3648915, 5402276, 5404272, 3154996, 6872897, 3034685, 6813239, 1078226, 6101522, 344678, 495751, 7995446, 5479386, 5961278, 4759670, 3566164, 4377043, 8007414, 5747008, 7561578, 4193586, 2449295, 6707004, 5073914, 6095819, 4994453, 5698380, 950247, 2371787, 5277843, 5637896, 7072035, 4519320, 4177253, 6456011, 3230181, 4709766, 6500089, 4159676, 4767674, 2090556],
[6733706, 926973, 7440093, 2663003, 2885064, 3493636, 6427357, 1756830, 5039307, 998353, 2988787, 4628476, 1053438, 5718420, 7992678, 6883699, 1556450, 85406, 1688332, 6903853, 4145683, 2748859, 3164167, 4643069, 3914397, 1302155, 3083963, 5254494, 4953560, 682047, 7131136, 4537490, 5718550, 5842111, 4523338, 6988827, 7811873, 5245118, 8017416, 2192129, 1374183, 4889032, 3431171, 2293299, 1457480, 4736841, 5354507, 5872480, 2154252, 6007014, 2564441, 8153442, 6260937, 2992747, 7203359, 2057538, 8221249, 2804693, 7060929, 7049215, 1431195, 64820, 564084, 2731283, 2704390, 7718181, 201478, 46170, 8230, 494290, 1373451, 4571303, 5528220, 2690226, 1371996, 5353841, 3331078, 5262318, 4885107, 3612338, 1976181, 5089590, 2018946, 5519631, 4993232, 3416794, 6128090, 6870638, 4208731, 2149022, 6410518, 5195682, 344330, 2950226, 1627439, 7488365, 3211341, 8035303, 4118832, 2398972, 148735, 5651689, 8214119, 6198613, 1023321, 2786768, 7540783, 311160, 4101310, 5528337, 5886986, 6638311, 6679982, 584065, 5181991, 7410612, 3364920, 1932601, 4777158, 5574736, 3285345, 7214832, 2647965, 4451462, 1406879, 6169307, 2147640, 3341243, 8051930, 3006111, 4535721, 3397273, 1314487, 8027588, 4079841, 6951762, 4256579, 1192584, 3907184, 7633046, 1081349, 2095698, 2277431, 6105975, 405985, 999111, 4841303, 7722159, 4455440, 5708294, 1801884, 6383790, 1053072, 5988091, 7074310, 5373736, 7547283, 5752115, 3756446, 3040104, 4813460, 1546330, 1375397, 4908092, 2348872, 6850981, 3424298, 3675312, 1972150, 1397566, 7689066, 799810, 2986955, 2074782, 169276, 1482743, 2854135, 2665423, 4381323, 7419214, 4860664, 1431499, 2906360, 7471026, 6768512, 5686479, 3720092, 7277753, 8079727, 1567202, 5577755, 4341379, 3009512, 4145172, 7165286, 2593006, 5273725, 5740670, 1150052, 161472, 2053638, 692045, 5807281, 6280107, 7369698, 6775551, 1292501, 7991234, 3077, 4142691, 7415860, 257257, 518440, 7681279, 6646880, 2017019, 2086642, 2028074, 3190464, 526045, 7157190, 5524062, 8047701, 2870297, 3035812, 4195318, 402281, 2105737, 5011264, 7881005, 4057032, 7532788, 5987844, 7312500, 4426194, 5359613, 7990876, 2687749, 7594478, 5199859, 461856, 1849978, 7894395, 6001856, 1454774, 539525, 3536419, 3571220, 4662650, 5395103, 5349732, 2861267, 583853, 6626729, 8053319, 748134],
[2454817, 2654111, 1548093, 3331115, 7110631, 5228083, 5381632, 5276749, 7956392, 5670417, 2663957, 4750473, 1362459, 2962448, 2393072, 4967961, 711658, 4644350, 273514, 7185683, 5437856, 7132513, 4912223, 1665383, 1243171, 127474, 364390, 5642901, 1395282, 5399613, 300887, 6316927, 5005855, 5514589, 5325362, 4103884, 4941082, 850095, 2775084, 7950590, 5585182, 4738665, 421994, 736676, 4446109, 5809950, 7893522, 259465, 1752710, 2093770, 7535098, 2037803, 1229871, 4952152, 2545739, 6405886, 3500575, 470314, 1963958, 5930725, 5966233, 8199, 7628113, 4324801, 3199543, 1244885, 5236963, 2677588, 8257582, 2439038, 3455394, 4600568, 1785185, 137921, 2315132, 1389906, 5354063, 3810729, 3558803, 4680613, 8149292, 7670013, 6686411, 4932944, 4808847, 4242739, 8277304, 3574825, 164905, 6305371, 6374874, 4645793, 4562891, 6434869, 5941350, 6659054, 7369577, 4392348, 6958802, 2476646, 4302330, 476360, 7681944, 2619043, 4023422, 7774336, 8304281, 2132253, 8284264, 6230539, 2565910, 6543489, 568236, 6630336, 7319376, 5644330, 5769111, 1578097, 7964882, 4528012, 1480245, 4916577, 2050127, 7847391, 959289, 4045223, 1659784, 2836440, 3510958, 4299979, 5824689, 92769, 3804707, 2052141, 4500964, 3000909, 4085247, 2933600, 4640594, 3129846, 1784480, 8053068, 4863506, 5708248, 5753904, 1396609, 2722747, 7356071, 4497561, 3470858, 5544708, 3158970, 1161014, 5441616, 6391013, 6773387, 4575582, 457951, 421591, 1860963, 2657400, 8225709, 6901474, 6964849, 1908143, 85442, 8075706, 2544810, 90829, 6855527, 2426331, 8030955, 6844494, 8197106, 2242622, 3011343, 4298175, 2837158, 1885921, 4204906, 8350276, 7177152, 5806262, 7932705, 7333929, 5915054, 5201159, 7628727, 6943460, 3144752, 5210493, 4176720, 3242375, 462009, 6638935, 6270784, 25279, 5262985, 2488123, 7622880, 145165, 1768500, 7938981, 5219326, 7274813, 748642, 8300935, 7756637, 5049200, 8258472, 2273281, 5898329, 4697463, 4665382, 2246597, 6733589, 1052983, 5997546, 4177345, 5110113, 6574075, 7632371, 7659434, 1935810, 7710511, 183803, 5249303, 3186020, 6405053, 7344182, 4538540, 4833452, 4057120, 3242452, 7895519, 7226931, 7934277, 2708217, 1044453, 2548320, 3340485, 988372, 6634324, 6532876, 2289995, 6862004, 3015559, 8236461, 919825, 6016163, 6328129, 3268893, 2154208, 988763, 931812, 7739737],
[3190135, 7552130, 1601955, 3921408, 4234491, 319172, 3982766, 1796468, 3882553, 4458250, 2867390, 2203516, 5759453, 8197200, 7887673, 2995827, 6663882, 5237458, 4968465, 5859994, 199073, 558308, 6772185, 7988335, 8347660, 7068531, 4107666, 3093546, 2781610, 4557541, 2273987, 8292276, 8207247, 7464896, 3838579, 4530350, 1966513, 7879485, 1533195, 5490519, 7850269, 5842343, 587729, 5174182, 729989, 7903980, 6828155, 373454, 5837869, 2493876, 7565005, 1469823, 2210100, 3701870, 3685948, 1476975, 6110433, 5220459, 512844, 6963587, 3105061, 8323615, 5371811, 6631756, 5736247, 6728753, 1995154, 3474744, 3568715, 4514388, 4215669, 5585756, 2751338, 7963133, 3331921, 5831353, 6329828, 6461770, 4426838, 4565127, 5472199, 5955742, 3211470, 5789758, 7541722, 6133672, 4331942, 2437080, 2695559, 6580250, 5177788, 3281125, 6108251, 3106393, 4706627, 7317195, 5181191, 5205190, 69069, 5518694, 6864461, 7399356, 5390356, 5802377, 4067571, 6270057, 2561689, 1280023, 7486364, 1575229, 1952027, 301150, 3288738, 7877139, 2896035, 4187940, 6321221, 2727052, 6338338, 6301255, 10521, 4998555, 1610093, 5493676, 8145784, 3688299, 4895726, 3785847, 1825123, 2029034, 5334857, 7969574, 1383624, 894253, 2053112, 4734139, 3085259, 2788864, 746607, 6480155, 3183676, 4143229, 2500876, 468320, 670146, 3176229, 7553264, 7981919, 3799821, 2056514, 38792, 718605, 3106793, 4429386, 5595766, 7113154, 2643131, 7788183, 2888436, 1095296, 3222375, 4745399, 2108271, 5043623, 8170855, 4821877, 6174654, 7041470, 5245348, 3074535, 3638435, 8050301, 2355645, 6124164, 4523011, 483255, 2364747, 6353621, 1835924, 6048351, 8306765, 2395107, 7009493, 7122411, 8112570, 6353850, 1007383, 6877894, 2097261, 5683910, 6913026, 5886720, 2951936, 1901371, 6639915, 6737895, 7557221, 4611566, 205354, 1985892, 3400026, 2648465, 7953012, 4661420, 2221717, 5558519, 872439, 2075264, 5157945, 846054, 8113103, 3945662, 2604934, 5636527, 3662793, 1066640, 5939313, 1320035, 6721312, 8313620, 7009337, 4040364, 6232471, 956787, 6278890, 4662552, 5360931, 7814362, 3791671, 6823707, 1707885, 1394806, 7447106, 3848695, 2319877, 7476950, 1976209, 8075311, 3456759, 5367907, 4541907, 7662872, 6910127, 1477730, 2782471, 2641709, 2838545, 6481096, 7078058, 4583203, 480204, 8036316, 1056789, 6111504, 4385333, 6740885]],
[[8296797, 52465, 3796610, 4724918, 6338244, 4474014, 6861150, 7123395, 6462707, 2156116, 302252, 5143124, 4672729, 2723696, 1513205, 4809722, 392635, 6260953, 4376325, 1621199, 7566820, 2402256, 2350919, 6901866, 6214530, 6146902, 4707007, 2846800, 6062097, 2556226, 2334820, 355844, 7943967, 2308723, 5828215, 3483839, 8369163, 2265685, 719419, 5479314, 8376888, 410826, 1954881, 5514184, 3014741, 4230103, 7882638, 2224932, 2579948, 1057999, 3106999, 678900, 1122746, 6061650, 915320, 1899937, 5306433, 6294680, 3708804, 1359341, 1920866, 4218462, 5174855, 539290, 8034540, 7952545, 3396743, 315786, 715585, 422636, 4708313, 5944192, 1504691, 4540995, 3976253, 8183573, 1883727, 7188374, 7480187, 6458377, 1833832, 1904657, 6573810, 6527718, 6797684, 2792119, 3372688, 197475, 3081304, 3326069, 933016, 6915525, 87157, 3566955, 5561823, 4391334, 6850825, 302461, 1819859, 3276938, 2205410, 591220, 2383039, 3145220, 6524616, 5501109, 2349847, 3308330, 3230333, 3744287, 67539, 1549072, 2517458, 1612670, 4082395, 7179385, 3980495, 7661295, 5737954, 7603431, 4616988, 6760561, 1078454, 1625653, 7391031, 7729592, 8203515, 1156572, 6693505, 3561135, 6317175, 2115265, 610583, 8049463, 2766019, 2759847, 6240704, 3597542, 6057458, 931019, 7686156, 5436057, 4355110, 868582, 4203800, 6900925, 6055936, 7268890, 7881802, 8236246, 3676117, 1630731, 676124, 3731037, 2070280, 3746310, 7057476, 127640, 7318853, 8288568, 6129911, 6297875, 3774744, 2915647, 3077752, 846593, 1269166, 7148232, 1961624, 4790554, 1262381, 6184733, 1233086, 5578104, 151828, 7150665, 261584, 4415038, 653358, 3204417, 6246525, 866475, 3141111, 5168344, 7938220, 7816082, 6287233, 4206433, 3692248, 7240662, 1025229, 1615594, 10434, 2016576, 7843666, 4803863, 3467860, 167290, 8228782, 6659193, 704168, 6980769, 7430686, 3259450, 1511381, 2139726, 8137077, 5040272, 7823792, 1678237, 8082110, 2973174, 7715844, 940139, 4645847, 5631332, 3489271, 2128100, 5168980, 2547952, 3215021, 5987665, 8242221, 7329471, 1078367, 4571157, 1239460, 4671571, 3275366, 996845, 7358108, 2252044, 2333546, 2414264, 3572730, 5520266, 136949, 7591197, 6978547, 1363458, 3528761, 2706727, 3638751, 8035696, 212784, 7175946, 913736, 8211430, 5698258, 75940, 7653532, 6994542, 136049, 1034039, 1189888, 7177394],
[4011397, 1880785, 7891850, 698409, 4245392, 1421663, 5599164, 1277510, 5558267, 1751136, 6596381, 2929773, 1809160, 7116539, 4458697, 5959246, 5808887, 2050918, 2856065, 6097737, 1710102, 3609626, 2001421, 6742971, 3495131, 4711150, 7094094, 3229215, 36568, 2512614, 2564507, 4854921, 802426, 4393624, 340352, 1622241, 7126958, 1563992, 8277097, 6809281, 3195081, 3580472, 2461629, 218079, 4034645, 1968235, 2147423, 8019177, 7320106, 8005276, 6123014, 7385593, 277936, 8194003, 5760304, 2107052, 2615622, 516367, 2312003, 5955034, 1787182, 8095172, 3887855, 4187687, 640638, 7978725, 8185562, 2516729, 540955, 6472775, 5193904, 2752296, 6582205, 942413, 2818961, 4866506, 2221951, 4277193, 2111115, 3432837, 6076292, 1741550, 7499069, 1426486, 4152569, 4014945, 6994698, 5650348, 6347341, 4425495, 5145315, 2069669, 8101131, 2357863, 5093044, 6421504, 3915715, 1648145, 573737, 7216611, 3304610, 543295, 1997414, 5258427, 3953101, 3737285, 485362, 8334765, 5846273, 4889181, 6509973, 2091367, 8316002, 2398968, 7094082, 4345092, 2023715, 5016001, 2066741, 7352303, 6327254, 8156523, 941660, 5927950, 2601983, 1781232, 4427151, 4959084, 2072580, 577716, 2082049, 3436341, 3014571, 6891829, 5585665, 5096306, 5294262, 2386899, 6163089, 908847, 1805291, 4173772, 3376741, 3427672, 482237, 1855052, 7040587, 4810549, 2986725, 473711, 97968, 5676435, 366074, 1089416, 1817365, 6764007, 3675336, 7204269, 7929132, 1899448, 4211272, 5632165, 3712828, 1730038, 7516713, 2693532, 8010246, 3973107, 7427354, 3072003, 1606352, 3225664, 5871929, 7627270, 5640982, 3307312, 1570649, 6117143, 6013270, 7594597, 4143351, 6339687, 4205094, 2251964, 1979594, 7168646, 6736897, 1969715, 6162236, 5064239, 2812894, 290395, 8374033, 2809324, 7309529, 3515116, 5566499, 6848541, 2722726, 6893953, 5697013, 1265653, 2070705, 7760124, 8051512, 5119045, 5477675, 7049558, 6093180, 414377, 4970539, 7689238, 715700, 5033886, 1760833, 1508880, 5611590, 4087846, 2404992, 3799644, 601293, 8142275, 1135114, 7300495, 4312734, 1279811, 5680751, 228961, 8206888, 2110767, 7133363, 615, 2784171, 1723225, 545532, 5256952, 2451367, 1057001, 3959077, 8367089, 3105540, 4260192, 7412107, 6198174, 190267, 6919189, 1641513, 39767, 401407, 1876430, 6020400, 349752, 1626705, 6360185, 3565951, 6461574],
[7242661, 2470069, 5236550, 4898683, 3901521, 1706173, 3238195, 2576925, 7946331, 3899093, 3958814, 5092598, 3460889, 5188442, 3344886, 7933696, 5618187, 3486648, 5401507, 7183732, 3072386, 3855609, 2166946, 8211287, 7847588, 346129, 7253175, 992541, 1885800, 6454056, 7212910, 411178, 6258102, 1472940, 6379857, 7894984, 7319067, 8251981, 4929366, 183176, 5274985, 6699842, 8130315, 224760, 7022522, 7131064, 2655671, 6171539, 1576773, 3208983, 7675099, 3808447, 2441782, 2540789, 3740587, 4814679, 127501, 1673257, 7808213, 1475951, 6173640, 1528466, 1715297, 4712258, 4570829, 5136737, 1440039, 1359130, 8279151, 4227998, 4933202, 5760163, 1501029, 6801753, 864623, 6596439, 4089098, 494110, 5677163, 5995642, 6273835, 7721657, 788909, 6528368, 7239432, 3569719, 4209787, 6636688, 5618759, 5585614, 6246865, 2579793, 1459357, 1104675, 7513439, 7183329, 3257485, 6997450, 2418496, 2061767, 5847786, 3386722, 4660701, 226639, 4955406, 3541723, 1691260, 5469643, 3834908, 5113344, 5645888, 2808875, 6367876, 6813493, 730558, 1491334, 6735300, 7895160, 3637955, 7564996, 2770288, 4197825, 6061488, 749232, 5913589, 6649071, 2325959, 5657166, 249478, 4609038, 1628047, 1253103, 4680937, 5959026, 7301248, 587358, 5777103, 4086938, 2839845, 1816696, 7298252, 5550779, 6727325, 7284704, 2002453, 6198037, 670468, 2048427, 4248366, 160229, 3324773, 2815931, 929610, 1902728, 4616306, 3534661, 7529627, 7067655, 1937002, 7794332, 6057953, 4337721, 4260293, 2380514, 6070674, 5401157, 7540558, 1674327, 6132784, 1526173, 5739052, 3910408, 7565682, 2283318, 3531899, 1053398, 3518631, 3714422, 5604765, 331482, 3558143, 1755623, 734583, 2760929, 6654248, 796839, 5883980, 6079034, 5440610, 1743370, 7927045, 4531030, 3033343, 1621609, 819428, 2825498, 6145759, 7378651, 1477412, 7963541, 4054114, 5301054, 1275412, 4163248, 908511, 8309056, 2220445, 1389824, 4032863, 5070161, 8308890, 14937, 5734199, 5918711, 2894529, 193871, 8134464, 2607961, 2564911, 5599637, 1550808, 5871491, 6401393, 1954686, 5952315, 1202311, 7031484, 7767178, 4034081, 8038307, 2844571, 525567, 6901753, 7960575, 4798256, 3736634, 2590754, 4860805, 7607562, 3860677, 2193824, 8267083, 7310705, 3283120, 2192055, 930838, 578606, 5876306, 3515389, 6906960, 2454694, 6012371, 4677636, 2412259, 4340453, 3332958],
[3505911, 7184931, 2529447, 2892114, 1629562, 2459739, 1895704, 5706753, 4492655, 4927066, 5213721, 3656744, 5019226, 7516993, 5454049, 8191433, 3813948, 3426775, 6513531, 2469736, 1562984, 5186466, 4665817, 4786742, 3415785, 6255127, 2554169, 5215110, 780494, 7871130, 375895, 3468077, 5318796, 7351551, 3124946, 6443316, 212321, 5503110, 5412495, 2536204, 7721384, 5019708, 8171830, 4245583, 5759120, 7682441, 1172316, 1697669, 2425142, 5543896, 4877947, 642232, 663137, 4874412, 4231703, 221093, 4555336, 4115713, 7251552, 1337221, 8289251, 2053093, 2885732, 2855875, 3149639, 6749170, 1659392, 4676314, 5772553, 5262624, 4724607, 5057009, 2758231, 5071162, 2535347, 5574263, 5300143, 5624747, 1889117, 20117, 6675353, 1986014, 181803, 6871879, 4557264, 3106176, 6816943, 5279412, 6076439, 2269644, 1066493, 8249304, 1109166, 4219414, 5919627, 6247029, 4202595, 7625770, 2281377, 2877828, 4319436, 962359, 5273366, 5981703, 7131647, 2099996, 6956147, 8350397, 5325773, 7155791, 2146080, 1575396, 1532020, 8363456, 3828239, 1174091, 732626, 7349323, 1781030, 7942615, 4726752, 2211115, 5830344, 8252253, 5426832, 5915924, 7428462, 1602400, 2117181, 102055, 6018886, 5100684, 5021393, 1672998, 2544832, 5906552, 241343, 1998955, 6472823, 6124461, 7347687, 6240982, 5908472, 2034293, 2608000, 841505, 6324289, 438669, 2700780, 4954901, 8163992, 5288267, 4322150, 7044808, 755691, 8176374, 951090, 2944246, 3035712, 4673144, 2270481, 1217372, 6335909, 6312263, 7106218, 3693369, 3000919, 1976092, 2394222, 2143225, 2088860, 2987214, 2091579, 6857401, 494799, 8105391, 4200858, 2005140, 1812145, 6624852, 4620221, 4570722, 6672221, 6834175, 4429758, 3007773, 2548817, 2107748, 3818931, 2955771, 4902632, 3354318, 4378419, 3964580, 6507955, 4631892, 2089157, 2334593, 867370, 3846517, 2526916, 5130749, 6834631, 7571674, 4948011, 7347184, 1796869, 4557037, 4454829, 4027642, 4159612, 4589377, 6151231, 1254383, 8355010, 405625, 6009586, 3936181, 7967204, 7934991, 8201408, 1069585, 641244, 6734521, 5111796, 1060467, 112613, 4731453, 6751114, 6588525, 7191414, 2645584, 2313006, 3744987, 5823595, 3596146, 7079604, 6295484, 2730757, 7238267, 5104939, 4322241, 3874663, 5944759, 5959364, 1158814, 4586884, 2865506, 2314004, 2562587, 327609, 7558572, 2587727, 4516592, 782658, 2374714],
[6154240, 8161227, 1989284, 1032823, 3770282, 4313432, 894454, 5407426, 4425522, 8204067, 4913215, 7547069, 7304786, 2301992, 348095, 7527717, 3808113, 3920770, 2083501, 3724409, 4100485, 7239949, 490753, 1167139, 5077771, 726561, 5503420, 4233409, 6525054, 3906085, 713267, 2698615, 7441514, 4884795, 2281440, 4460298, 7687557, 6561047, 2553713, 3410646, 1408349, 8281991, 2394833, 6759649, 4222522, 6188806, 7175228, 1190286, 638154, 7049699, 3773145, 7661603, 2227353, 704261, 2515917, 2452610, 1459786, 6963825, 2905124, 461491, 7136043, 1131818, 3683261, 2970970, 4905391, 5977164, 3701882, 2978278, 3805595, 4134999, 4583937, 2513828, 4820174, 7050428, 8069545, 102197, 1968458, 7818406, 4299114, 7515, 4818964, 7094493, 4127825, 5055201, 8250897, 7569772, 4840709, 3132201, 331053, 4505244, 6706392, 5770305, 7788677, 8027447, 5502719, 811225, 3836400, 3269461, 2804851, 1459783, 1673839, 7689794, 4083429, 7063986, 4371419, 3289764, 3461882, 2155159, 1422073, 5699703, 1926725, 4624875, 182223, 2349464, 6745080, 8216642, 421826, 4804320, 1367180, 6839134, 573159, 1194852, 1767000, 2822989, 6797943, 5938358, 7792049, 772187, 8010036, 4298904, 1080631, 6563672, 6369503, 1645315, 1260527, 1667032, 8185233, 2428027, 267963, 3900128, 3687897, 2608044, 2170066, 7732369, 2335704, 4991888, 4827652, 5408511, 4243649, 6743838, 1021939, 8127823, 498709, 812812, 3649154, 4785820, 53465, 139224, 407056, 2015216, 6972916, 7393262, 868994, 1983513, 4958237, 3552805, 2618798, 5861970, 7018071, 3387644, 5619011, 5221105, 4839035, 3234713, 7421800, 143374, 5228816, 6551470, 7020970, 2187954, 90063, 2619584, 7851879, 7038980, 7912038, 4921891, 360632, 256778, 1711198, 2778635, 1920775, 8161303, 1738076, 1638269, 5224387, 6961619, 6985735, 444258, 1404680, 1404545, 3753465, 7544669, 5222208, 2451112, 5407583, 5615888, 4023470, 5925234, 7943785, 5126170, 5062475, 7387155, 6819251, 1869650, 4425621, 583749, 794838, 643852, 5701412, 4006240, 6738597, 3202611, 31685, 1513662, 4337275, 3330330, 7422396, 2846327, 8283705, 6612658, 5772528, 5026842, 3774040, 3435572, 6045175, 1420524, 6300166, 7056615, 4088882, 2310628, 1775221, 1739665, 2050395, 1665453, 8314231, 4758613, 1509778, 1375601, 8359013, 977695, 6619493, 2405705, 3461656, 2849045, 5373646, 5108244]],
[[4123598, 3448406, 409178, 5239529, 209278, 3671193, 3643642, 2596393, 5298400, 2983678, 5157812, 1444846, 283343, 1520174, 6834720, 4262079, 5110560, 2426763, 3948636, 634725, 97289, 5146003, 2166085, 5365165, 1330288, 2617602, 3550644, 1472027, 8295525, 7645260, 3450572, 7176247, 1012166, 5910995, 1004783, 449953, 1943922, 5607533, 3686994, 7024177, 5022701, 1971203, 5892232, 80008, 8101920, 829482, 2475390, 1018230, 4077099, 641636, 5352337, 6250566, 3441343, 1156448, 518794, 7745530, 2028058, 4792750, 5850713, 594571, 7580202, 5616200, 4066597, 2016088, 1728687, 8064358, 3805310, 5760607, 3247037, 2013056, 2209595, 837861, 8129218, 6979696, 2988400, 5025307, 2546927, 6054250, 2881425, 3674257, 6523852, 2406871, 1516120, 3550300, 5871896, 1937255, 5240881, 8232859, 5354836, 2816386, 4413999, 4468819, 927849, 3855341, 4568972, 7715582, 6387547, 6125511, 8278269, 6145994, 5320938, 4659835, 6863759, 3231568, 1250250, 725286, 3314146, 958310, 8369979, 7565120, 1929370, 6508263, 8332666, 1655602, 3306590, 6912767, 7439730, 3466723, 2745751, 330516, 6490851, 7690926, 2005103, 223431, 7006174, 1155333, 3557365, 106083, 3757385, 6165340, 7397247, 437478, 5388882, 239171, 5194521, 1606449, 5823022, 4088534, 5931866, 8238717, 6869604, 6185814, 7088650, 5630624, 3004552, 1858827, 5036901, 4067288, 1207436, 5134367, 3484254, 879519, 2434205, 2749688, 2775397, 3050206, 6064647, 1878545, 3669867, 1964839, 5136285, 5351679, 16043, 7275296, 3061054, 1164118, 2104438, 6263990, 5634773, 759721, 6335552, 1213862, 7871378, 7678032, 8097538, 554176, 5283848, 4202148, 523569, 4044848, 7708947, 4274339, 492753, 5734967, 2630844, 5186067, 4263924, 1585355, 1064721, 7552641, 2260202, 6418520, 2777062, 3445214, 416070, 422444, 306004, 4703356, 1134153, 3356631, 2258779, 4108818, 576709, 2585881, 6171747, 7862623, 5896126, 5426582, 2469836, 1003451, 1334491, 4535612, 7997213, 5950880, 837686, 2383589, 738657, 402666, 5177602, 8010990, 1367751, 1392328, 5425255, 6109262, 3730113, 3425498, 1903454, 3874746, 1352306, 3628758, 5391774, 4461202, 7662152, 4462161, 3999953, 419736, 4132698, 1096386, 3740208, 2258929, 2116021, 2996533, 5964414, 5034264, 5157879, 5639518, 6308734, 1463336, 6155318, 5584067, 673956, 7785186, 1730492, 3623038, 6746927, 8327857],
[3185588, 488481, 3568944, 6712693, 3038580, 3399302, 2356845, 2988312, 1720275, 7843921, 3783605, 7793814, 2228015, 715506, 179352, 4579525, 3468987, 2958017, 1203831, 4818099, 5526682, 4801360, 2465844, 4609521, 936908, 3841796, 1400246, 4369381, 2970689, 4041005, 3723904, 4439576, 3487682, 1074105, 3808925, 7458931, 5218679, 7988633, 1572490, 7530654, 7826675, 1495455, 4745515, 3639789, 2964750, 7408789, 6467417, 1756164, 3833194, 7492869, 5750017, 321987, 1403817, 7844579, 4270895, 6196241, 6065428, 5424081, 1609779, 5555268, 821876, 3880951, 4303389, 6784567, 7508172, 2626536, 5910970, 6491338, 3755930, 434111, 4742022, 330526, 2600020, 740244, 2113852, 3987855, 447467, 2355259, 3617094, 959743, 3684343, 7681647, 3815841, 2953820, 5316435, 3472828, 1758947, 3804955, 1077119, 7391176, 7715164, 8286929, 5098629, 457848, 4386222, 1950300, 1735047, 4621724, 5957584, 6511521, 1660171, 1233346, 5307183, 2152001, 449989, 7485850, 8349334, 5730599, 1420643, 1737255, 8163645, 231902, 6367878, 7704868, 190373, 7273546, 1976464, 2306090, 315701, 7847998, 6671723, 6936917, 4520790, 2662017, 2219284, 1690757, 5984140, 7489744, 6783790, 5856912, 4219307, 4673108, 1437098, 4372043, 5021396, 1089645, 492102, 3860922, 1125168, 3283472, 5289231, 3485031, 4041006, 1309175, 2042426, 2700451, 4995969, 8345305, 1838285, 1947156, 5317271, 3136672, 4823237, 3021237, 5905597, 2803517, 4259469, 4651749, 4787257, 2206562, 1884876, 3978686, 502751, 6722374, 2782515, 2101518, 1304797, 2634176, 3956146, 3583849, 1539269, 6015308, 5343563, 1766547, 7613644, 1083113, 6832353, 6757958, 7359307, 2971553, 112489, 5476402, 2078742, 2814554, 1284809, 544592, 1405558, 6644712, 2136272, 6189329, 6595619, 7450101, 274601, 5455850, 2076841, 3547529, 6076927, 6040531, 2637603, 6948156, 6799036, 1780484, 4969497, 5849043, 2003889, 1660066, 2286193, 4820813, 4541356, 4547855, 8068842, 8051337, 7797428, 3941367, 6427095, 5779887, 6550171, 7212201, 6889058, 6629268, 6417638, 6968902, 4826353, 1643325, 7157630, 5390900, 7744198, 5306165, 4287474, 5764530, 2893992, 937735, 2736253, 4435118, 2089203, 997671, 1718857, 5449334, 5006265, 180474, 2429545, 1572388, 7854684, 4144968, 1381792, 7581323, 1236058, 6264179, 1576597, 338181, 3819790, 4637370, 3478861, 3842218, 3021586, 6921086],
[6552663, 1280010, 1169216, 5565237, 7336378, 7138113, 3680077, 1791355, 2777797, 2140176, 6059983, 4083330, 1628809, 7309540, 5678342, 3533241, 1447593, 948139, 6446717, 4748463, 903758, 4427875, 6622757, 6033037, 505563, 2982629, 5255780, 6558809, 6551671, 2903617, 7390305, 185073, 2978483, 1036594, 1895800, 552509, 3419732, 4541321, 2030304, 5208061, 3794427, 2798339, 4730715, 4029486, 567153, 835820, 3372801, 2146619, 7359721, 6324549, 5223353, 7138870, 2333131, 4502548, 7503677, 8102162, 1236299, 903173, 7312172, 7757503, 6851285, 2232335, 1167418, 1174598, 962181, 6918235, 6997289, 5032467, 1025834, 1629012, 2061567, 6999689, 3658364, 1344117, 5900806, 185798, 5302778, 4708164, 4121075, 293801, 4150892, 2602470, 4906926, 3629131, 4298552, 1831020, 2819659, 311999, 5054183, 2581534, 3746286, 3461614, 4883183, 3471737, 6673642, 2597790, 4817763, 3419693, 6593184, 1061106, 1588959, 1426272, 5149212, 3672802, 7609448, 1968781, 310953, 6189308, 1867278, 2811822, 8287296, 10195, 2982587, 7955958, 5011419, 7318909, 5406970, 6746527, 7043486, 8222975, 5981853, 1416455, 1445363, 8097299, 4991252, 5483231, 4573877, 7352686, 3191603, 2684578, 1766089, 4370575, 3793458, 6261541, 5776024, 5443223, 3862534, 7619607, 1873612, 5774996, 6993231, 8268105, 28072, 2825736, 7626778, 2252302, 6196282, 3858562, 2812735, 1281733, 800694, 1597656, 3804882, 6537303, 1231529, 4244657, 886175, 1527195, 8306011, 2051575, 6606310, 3131689, 1322514, 2004521, 5106163, 5845943, 977121, 3592983, 5166274, 4875953, 7122315, 6735578, 5171051, 409943, 568887, 4877752, 2951778, 363983, 2005203, 4952471, 6440868, 2149243, 726413, 4841599, 316288, 5756468, 5337985, 4895400, 7637215, 4928236, 7425657, 3713805, 5070325, 219511, 2125536, 6040392, 7089746, 1814703, 4773438, 5552985, 6421542, 245585, 3516448, 7474753, 5764155, 2399523, 4546609, 6103743, 6856673, 7824930, 778655, 5287374, 6048985, 1401386, 2697217, 8323030, 7127082, 1927224, 6662013, 6739578, 1507953, 1837563, 5753198, 8340383, 2338114, 6070860, 1729497, 3142242, 6179970, 2007187, 2198796, 6701707, 8173811, 5228840, 2693762, 7784040, 4166460, 1710578, 6138273, 1955424, 7260184, 235902, 3543881, 4994822, 3324208, 3215092, 4884428, 2569959, 5156810, 5343511, 5527783, 6759878, 4053003, 4195847, 211091, 3277845],
[2965831, 6464184, 6220847, 4639673, 4071494, 6052078, 1999211, 778783, 4861874, 6630001, 3070811, 3753690, 1741434, 3094164, 7569147, 4398394, 42081, 6317064, 8060020, 3967826, 6187996, 6394524, 4072532, 5978637, 1205528, 3832132, 3812774, 593054, 7328783, 8352738, 4342430, 5084221, 8213842, 1554792, 8176326, 3297673, 7948630, 5363361, 7440298, 7569979, 3401706, 5043617, 5206776, 2032918, 3422241, 6908037, 1199797, 8268800, 673784, 6373893, 8049886, 4994978, 3071116, 327989, 4640320, 489372, 1177168, 2829593, 8315926, 5949626, 1470636, 3427683, 4604436, 4425048, 2307002, 6867978, 475502, 3024359, 2021056, 981093, 987776, 7137459, 7501086, 4051622, 2132174, 6453532, 7561898, 7737305, 7755764, 1334781, 7713050, 2692930, 2841067, 503817, 7855654, 3345424, 3535557, 7678360, 6290046, 1918547, 8124207, 1523664, 8100762, 7195977, 3231302, 8310873, 5645080, 3559684, 1128187, 3891897, 3015627, 7478597, 8298570, 1251562, 6210145, 3007629, 3552333, 1668968, 4981441, 3372264, 6299985, 3194639, 7038928, 5624467, 2525976, 763101, 580453, 7174653, 7967082, 3604333, 7983896, 3677884, 1559651, 8307424, 4213601, 4045827, 1955831, 2391845, 4186029, 7245229, 6894608, 4808076, 6231238, 7560744, 1805759, 6689618, 5090615, 6860441, 6873901, 6754048, 5441655, 488540, 202765, 1612042, 8013229, 5596096, 6596955, 6213129, 8232359, 5682369, 2937800, 5729939, 4457651, 5558770, 933226, 6432813, 992336, 2124073, 2022624, 6571915, 7137115, 2069643, 2380853, 1372342, 7200675, 2361893, 1488869, 2248504, 85594, 3917010, 5863792, 3355277, 2811831, 2084618, 8372073, 6765822, 1787230, 4287599, 1706747, 1803615, 4247632, 6028413, 2136468, 2473945, 3430566, 6815475, 3144360, 7895, 6995547, 4465295, 4803469, 7810195, 1668094, 2883785, 3694501, 1038120, 2799891, 2102185, 7297303, 4577109, 3343111, 1729277, 5694159, 4048848, 360468, 6077984, 6308176, 909212, 1031483, 1433454, 3106136, 398199, 6405713, 7488648, 488550, 8226186, 4184984, 543623, 4183547, 3512018, 739176, 6989059, 400730, 591652, 2764072, 4574056, 4857244, 2428413, 6584201, 5272703, 5622580, 7435132, 5069049, 4104612, 7221237, 2306544, 7594042, 887902, 1797558, 3173212, 6271783, 1434674, 8303947, 8111691, 3412665, 3931247, 2819462, 2144686, 4865606, 5838132, 6120503, 2237882, 1202307, 4339660, 7090192, 2610504],
[5171774, 5528645, 7147189, 694376, 6300248, 1055924, 5096868, 1609486, 6983216, 5950987, 7490641, 6305492, 4152301, 4540158, 2393363, 5959418, 5698612, 5993755, 2462200, 5724300, 1193239, 2820171, 6276093, 1922836, 6103783, 1894028, 2497604, 3335189, 6065851, 2661408, 31243, 7108049, 6295766, 804279, 4812724, 4923796, 2085790, 2431822, 4151446, 3049153, 471097, 5714320, 6798582, 721542, 136747, 5295584, 5919325, 3868866, 2171645, 2432543, 3902147, 3957795, 7369654, 7192073, 3042823, 4476731, 6915565, 868694, 4045156, 3479017, 5777630, 42697, 2572683, 7249586, 2907578, 4179591, 520530, 7527254, 5554232, 7242836, 6345720, 4499015, 1230206, 738646, 8174481, 3436983, 6029173, 5264076, 7757728, 1647592, 7969805, 3068809, 1761444, 8180574, 1034042, 1429457, 4232485, 4937818, 3850132, 3028583, 617738, 2617117, 3484013, 1560101, 6387824, 6844402, 6535791, 7026894, 7467033, 1155954, 5402841, 1959569, 7569183, 747946, 1552365, 1229873, 3438493, 8161870, 592679, 5434633, 3047597, 4900112, 7448584, 4062938, 6316564, 4814622, 1430005, 2860760, 5152027, 6563896, 2362767, 5060318, 1069988, 6730612, 815508, 5998345, 4834409, 8065744, 1942659, 4829435, 3782488, 6569463, 2213526, 7331561, 5047502, 642400, 6009838, 4996498, 542568, 6252927, 5433748, 6741178, 2781026, 1282900, 1725100, 5374492, 4698334, 3245752, 6845253, 1195724, 5141169, 889262, 7934799, 7382205, 2219138, 4173949, 2979485, 4326332, 2803356, 2601740, 2215595, 7465296, 6052308, 2140978, 5849680, 4258951, 973630, 5934160, 3176647, 4351827, 1572722, 4701843, 1906531, 1591742, 4456761, 3299111, 456517, 6479359, 6843770, 5375150, 2214876, 4591930, 3993471, 1298360, 5138523, 2997131, 6185221, 319961, 2982420, 4401772, 4174447, 1527432, 288681, 4814121, 2978539, 2502590, 1828779, 7343302, 3825663, 4315460, 1536937, 4757983, 2178102, 4188256, 376383, 6160630, 1062086, 2318881, 1212361, 6889464, 6954949, 7129856, 2345292, 1166356, 5898347, 4974479, 888653, 4854837, 915893, 692280, 2723128, 684561, 2393399, 2514570, 6611440, 6419424, 1002208, 1004612, 8034182, 1175085, 2129937, 3071873, 2712968, 4035060, 4314614, 7482215, 3285279, 928303, 2413892, 7711025, 5714494, 4419320, 3722286, 557272, 6182142, 194323, 4331269, 6720331, 6174196, 6728339, 2147690, 2647344, 1625912, 267573, 3096528, 4250855]],
[[2941963, 4906494, 3816182, 2633411, 6817580, 1066628, 4034403, 3079405, 5757861, 5898895, 8114637, 1821109, 9226, 389653, 1921682, 6772061, 5467254, 2714212, 1361565, 8296248, 5058256, 835776, 1296532, 8333089, 4277294, 3009471, 8166104, 4537965, 1941493, 6542327, 5433245, 1874484, 8279042, 2272526, 7185446, 4313653, 3149739, 224625, 5501545, 5987940, 1156907, 585055, 7703853, 2462403, 4226775, 7883605, 1689972, 972813, 2715652, 4485448, 1497910, 4815474, 330097, 2674130, 5734767, 1710006, 7409709, 625496, 4839243, 5229172, 3201132, 6046052, 7193568, 6992064, 7384407, 2456603, 5870424, 2997216, 5533461, 6486557, 7901117, 5925707, 7665481, 5405023, 7000918, 1179971, 8254369, 4084681, 1739177, 2994980, 2574061, 2594944, 1998671, 1389416, 3942671, 7152749, 1659002, 7995826, 1181482, 6888231, 18391, 3655369, 3574704, 7194385, 8114959, 4068521, 3672314, 1958334, 1404388, 7227453, 6723366, 5143257, 8111799, 4193128, 7393542, 5548729, 6948619, 6064275, 1542342, 8374313, 1770054, 1811317, 3559694, 3725247, 7759082, 394878, 3789982, 2100146, 4883090, 2618941, 4533357, 1837690, 4588701, 2977315, 6797076, 1739422, 5031485, 6549877, 6700914, 4912553, 3007084, 6157040, 5104250, 3737932, 2779705, 1333558, 7038269, 555558, 4363657, 6039756, 7652300, 888829, 7155964, 2858345, 2505358, 6175130, 1278923, 5312413, 6372954, 6777569, 2691976, 7451595, 6159782, 403127, 5441604, 4525536, 1048516, 4353001, 5264453, 5203949, 3183905, 383849, 3088550, 5823423, 1686275, 1109303, 8365683, 8200435, 3078238, 5677043, 2218107, 3161278, 7413823, 423620, 3546765, 6508302, 8145474, 5483606, 8182398, 3932545, 5682246, 8206759, 2107610, 6823670, 3458918, 2021413, 1280965, 8302393, 1791190, 7253326, 5902115, 1225989, 1323834, 8011522, 7989784, 6159945, 4593282, 1883923, 1453887, 6735114, 956408, 735855, 4386316, 8274603, 6111581, 7572133, 3107685, 1024936, 4769201, 2107145, 2049843, 4127798, 6922073, 3094822, 1045263, 1361090, 3864671, 3360729, 5130963, 5009258, 1381583, 7663068, 3385089, 8239781, 5917865, 7140706, 3177511, 8224080, 6782166, 7221038, 3011399, 7063681, 518007, 7925332, 5188734, 7322190, 7029820, 6021497, 4613917, 7342742, 2039704, 4703136, 6056974, 1425963, 7059621, 3902133, 6649936, 2444131, 3991344, 3112611, 4285077, 5280722, 5086047, 5728445, 1556325, 7357531],
[3318031, 7263249, 6067456, 5572440, 5286758, 4756364, 5941133, 3853290, 1286825, 5275955, 2063909, 794596, 6100290, 3387868, 3523726, 488671, 3348517, 5522265, 62638, 5081048, 7185718, 7047547, 3108847, 318636, 3798230, 1722664, 1956836, 7394631, 1977483, 624227, 7875007, 4555688, 7578771, 3830913, 2144420, 4920123, 1249479, 5829104, 4595863, 1923232, 2844209, 2508850, 2485585, 2396989, 215600, 6995502, 6415924, 7710747, 4319506, 4476671, 1698979, 52777, 5555598, 6767068, 11263, 6905133, 810033, 5597588, 5841687, 4010359, 2159922, 612059, 4850787, 5526881, 3620600, 4802139, 1539207, 7295260, 2081086, 6067254, 6699221, 6599650, 7331679, 135097, 3432330, 7190985, 175510, 5615961, 1543660, 7791779, 6955941, 4350891, 7759036, 5443616, 7392223, 3608551, 5939286, 6825171, 6983724, 4833643, 7023295, 3642829, 1718665, 1732540, 4353546, 821223, 74564, 7624158, 3124516, 7621103, 6441342, 7851511, 1347050, 4169873, 7086617, 4408310, 6358477, 7090930, 2232973, 7578943, 5552474, 363405, 386622, 3820948, 7098886, 4612146, 3618811, 3731621, 5025968, 7886334, 5323745, 3860679, 547742, 2993614, 571164, 5283779, 6206835, 2494589, 1384221, 4741850, 2643711, 2650516, 4456474, 964124, 3467237, 4555051, 2737378, 7248509, 8244478, 2707521, 5868042, 3840342, 4097636, 544759, 4899486, 7648712, 3812582, 520357, 1274483, 3374597, 3498217, 7001293, 2072520, 445502, 1012694, 6024331, 1792373, 4257420, 4662905, 5135470, 1040504, 1551190, 2348171, 6845850, 7706501, 3794097, 6329511, 5679447, 2719495, 2781028, 2453345, 5242841, 6410101, 4103910, 6008180, 4950142, 5950641, 5907023, 4117529, 3063420, 6988757, 4233342, 1907404, 6691705, 2713388, 5404111, 5912961, 4619316, 6182250, 91567, 6423979, 6900112, 135229, 7030752, 6890571, 416188, 6664784, 4316783, 2480741, 7528309, 1683324, 4872621, 7664388, 2956869, 6406936, 2741828, 1561814, 447098, 1443814, 5479710, 3699067, 406794, 883298, 1417795, 5030668, 7768289, 4354493, 1764965, 8181010, 5507409, 6555513, 213248, 7316779, 5538503, 6672891, 7041123, 1941917, 4864348, 5619531, 3694604, 1940353, 3253664, 1164658, 2687764, 8207744, 7726475, 4222250, 516025, 2814668, 2606556, 4225241, 6605085, 6786768, 4931400, 7423443, 4113197, 2886338, 4422718, 4347952, 3854055, 1646715, 1039161, 6618308, 3987990, 277844, 5025591],
[506881, 4970359, 6738252, 6423443, 3871730, 3346046, 5480162, 8126568, 6397770, 2033150, 7120010, 3780202, 6352270, 2845839, 4280367, 4264186, 535564, 1446787, 958333, 5237752, 4009418, 5512419, 5073745, 201691, 8254374, 2207277, 325061, 4564040, 5216272, 8371667, 2330852, 3107288, 5389605, 3881694, 6722905, 1621308, 7413829, 8365669, 2462605, 183492, 3338213, 1938152, 1048959, 5495755, 5234219, 5326320, 2671357, 8198635, 3807741, 5615696, 7398160, 7166552, 8240671, 3879479, 1460940, 162244, 1639767, 2801666, 5646136, 6706561, 4183259, 3122812, 7606594, 7375062, 2876129, 366006, 229698, 1080556, 1900869, 350651, 2365328, 7459179, 4456307, 6200668, 803092, 4488424, 1409082, 3516159, 4012453, 5366198, 3538649, 5123232, 6579140, 5940190, 7838406, 5099518, 1217372, 7567847, 269993, 7573849, 7149458, 5845634, 85043, 7240572, 8028786, 93109, 6626471, 3610836, 7030114, 2594356, 8299226, 683463, 6988529, 464138, 5062242, 5797064, 5613439, 6488687, 6536306, 5881629, 6172075, 1567211, 3168812, 3844569, 4513626, 1048432, 3357271, 6237599, 1821115, 1632714, 7423810, 7867217, 4675698, 2544302, 5477623, 8062272, 8122415, 5472546, 3299238, 7462564, 8068696, 4481649, 5342038, 5033188, 389893, 3796944, 6944625, 1928162, 7206151, 5313900, 7619354, 6139312, 7873033, 8074724, 1231786, 7271668, 1206237, 4199249, 2405000, 4020298, 4541084, 6134245, 4782152, 1039258, 5683958, 360752, 1072139, 7654236, 3482850, 4562501, 7737412, 6790930, 7223341, 8145896, 2433887, 2792976, 6017162, 7467671, 5305901, 5185366, 838081, 2657613, 3980371, 571892, 3884058, 130063, 6540574, 2866810, 6599140, 4367637, 5653590, 4351071, 963540, 2448266, 3016290, 1675696, 7631763, 6489165, 8057500, 921581, 2794620, 2605132, 4120794, 5915418, 2576792, 629531, 6569735, 3898715, 3618462, 5989681, 6017584, 1265443, 2150403, 3605948, 6401763, 3461887, 6621831, 6709195, 5002772, 6806554, 282130, 7762381, 5255550, 6671316, 4059370, 649951, 5159215, 5730512, 561758, 6246360, 3977255, 640143, 1268152, 774605, 5084123, 5972801, 5937807, 8123409, 7182819, 8081083, 383099, 131835, 6777922, 1745461, 8262027, 6029722, 5079903, 4548819, 3542779, 8181959, 4338235, 2021363, 3037183, 758874, 5802859, 6258826, 8283821, 5299605, 7551387, 675025, 3481063, 4317285, 5529292, 6375260, 4150728, 4078723],
[7621243, 6577159, 7557357, 6085108, 5145785, 3459585, 4648298, 3165694, 4371587, 6494215, 843885, 6494893, 708085, 2263116, 5198727, 681907, 2140515, 7934983, 2818308, 7374287, 3158131, 7626845, 6044614, 7655853, 6677786, 1224760, 2586900, 5483256, 3316094, 4341995, 3981251, 7390940, 7749842, 4624324, 1910366, 753429, 4502234, 8098000, 8150364, 5879299, 696575, 4462259, 758980, 8340498, 4223945, 3368154, 715936, 7220902, 6547269, 7137505, 2863711, 936445, 5585682, 6058285, 4732606, 7916727, 5396972, 879133, 2896943, 8378787, 5770043, 3372853, 1857873, 287575, 4120615, 5077612, 6255748, 8098148, 2623475, 6432000, 5215998, 209862, 1061516, 5231530, 4831446, 1589722, 5643248, 2116923, 4723429, 2406537, 544032, 885854, 7531295, 3159680, 2850208, 7676088, 7811173, 2177616, 5614018, 4836909, 3990738, 1128189, 6624474, 6835563, 4549655, 6187966, 3431822, 1996432, 5993673, 5297409, 7107228, 192697, 3342873, 6889101, 5075392, 280343, 6750337, 3831151, 1833245, 5995214, 3038925, 4609911, 4570779, 1060211, 1199186, 6757682, 3251307, 2416742, 3757176, 2854319, 258741, 7850418, 7186071, 4568324, 8014605, 5221229, 5695542, 7308848, 1785078, 4556882, 3250917, 7720926, 4588619, 801807, 2171205, 2709127, 7994835, 3404424, 238604, 5866514, 7422482, 1644486, 2723401, 7879034, 4495024, 7643517, 1051301, 5702770, 86624, 2661618, 672899, 2888358, 6221138, 5887165, 7516703, 2055291, 7050682, 6178117, 3979861, 663400, 2800383, 5829403, 870758, 1718351, 7092888, 7899747, 2716600, 5076512, 7100674, 500421, 1461965, 4359331, 8357709, 1611169, 2168144, 2315299, 1647538, 906195, 5594423, 5012987, 6561962, 6448297, 4775887, 7656975, 3663632, 2613656, 1894207, 5086980, 4854532, 3999538, 4666441, 2806561, 8100506, 3649642, 533881, 3268912, 6078585, 3064439, 6114264, 127088, 5819265, 18776, 1582697, 1117502, 7811452, 7808618, 1279691, 6438230, 5862731, 7448229, 7153089, 385289, 7318227, 1929658, 5260475, 7932418, 6737967, 6667591, 269489, 6887105, 1058540, 5441073, 6428826, 7527141, 7026552, 2154562, 6470606, 6650124, 1948395, 8007155, 2996866, 4527087, 1856838, 6080714, 2128791, 3118479, 4536152, 5961313, 7927575, 954594, 7260493, 6122119, 3519256, 642811, 1985012, 2565446, 1010485, 4727514, 5947186, 1629822, 6322202, 4605249, 492560, 1393608, 7947862, 765160],
[2764987, 8265754, 4085653, 2571110, 5874556, 4816797, 4307803, 2903115, 2213523, 7564542, 609540, 3218825, 2966901, 6953123, 5040158, 3634905, 5146721, 1037657, 3730957, 838667, 230042, 6642499, 165410, 8179222, 698780, 5242489, 3420628, 178230, 3898587, 464125, 6347376, 8144542, 4076293, 1048449, 6149946, 4939334, 2693087, 6308445, 1085833, 6960106, 7244803, 4420512, 7956846, 5059881, 7078820, 8039565, 699220, 5893296, 896122, 5868065, 7640105, 6537027, 4880568, 5529625, 2061696, 2626772, 5799951, 7806434, 14084, 7932250, 4442369, 3943994, 4831760, 602700, 8152073, 7816638, 1359389, 6882576, 2763304, 2910766, 4646339, 1130064, 3414945, 5228190, 5002151, 3800008, 5298575, 2038122, 6276288, 7664888, 5574450, 6534336, 4785282, 6753578, 6591880, 4644286, 3504227, 2470756, 1796982, 6302889, 379217, 2708101, 1597582, 111366, 590930, 3766372, 6343003, 4151100, 6938387, 3575052, 7482105, 8325644, 8346687, 5084652, 2807324, 8089836, 3985020, 8067932, 5224509, 6791771, 5535586, 874381, 7177934, 6534199, 6713887, 1943324, 3857854, 4152662, 8317549, 6030090, 6712551, 5286076, 7572436, 478595, 6885836, 5641452, 3173931, 5623281, 3985962, 3694513, 981855, 1135237, 3919842, 6293519, 4793791, 7486070, 3367029, 6723767, 5026578, 6856587, 5147259, 4576874, 7795001, 5439877, 5628512, 92895, 2752363, 5546504, 1471928, 5915958, 5667211, 5663425, 735546, 5982127, 7345069, 4160592, 6146734, 4627332, 8196929, 7017553, 2694026, 2574703, 7543660, 4006984, 4331236, 5470194, 824121, 6676793, 4390051, 5928793, 211188, 4476257, 8111375, 750049, 1091232, 3613381, 5633748, 6176660, 2886483, 8178155, 8228572, 7440866, 4993137, 4500499, 2283872, 6101876, 2270564, 7809342, 5787031, 2520603, 4515582, 5945459, 7068686, 5924947, 1217119, 5165408, 1692462, 2473134, 4471647, 5336995, 2478154, 6241745, 5766193, 6354325, 4469677, 1533044, 4932803, 5106364, 1331374, 7358345, 5101658, 5502078, 4178800, 1485314, 6035300, 1437937, 4120042, 3713826, 3814953, 3584189, 4015595, 7139275, 1843053, 3775132, 7286957, 4877081, 5352435, 2182792, 1905248, 6759565, 2123526, 6755218, 5856818, 4176312, 7940722, 1916122, 1566401, 1234815, 7823963, 1280422, 6814404, 2758353, 7564833, 977365, 2282376, 5029440, 2756237, 1645766, 502738, 975553, 3676720, 483054, 3944675, 5879715, 6035883, 1178946]]]
trCandidate: D26AF4F24DE50EBEDA020DFC6F841B0A2D83D2781C06D8B3DF8EDA97A7EA4F9913ABEE9858F88F8A2F52C13DF2DE4BA023BAA5B3CB0ED941E077A08AE3F14035
muCandidate: 6306E6ADBAAF5509B5C86CED5FAF3F5D168FB8BFD7C4704E751F7D7AEC3ECF2D988D9A64516854341789E6D53E8CB9C713E68B25F35C2BB99B34208CE29D1F43

c: [0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1]

NTT(z): [[5355856, 836771, 5926131, 1698606, 3996443, 1349399, 2432415, 2945189, 991111, 7368239, 1969006, 5103307, 4606079, 1179943, 1117008, 1133122, 3831074, 7860746, 7310157, 6461064, 2724959, 5189982, 4947289, 1730930, 3216955, 4029963, 3892870, 3745414, 5021041, 3665806, 1088554, 6102570, 5661184, 2027827, 2673779, 3098961, 4914648, 2555543, 2027364, 5511540, 2618482, 2753042, 8220303, 5106732, 1696202, 2832871, 2865549, 4434898, 7410634, 94929, 8369290, 7396882, 6835275, 5998172, 7490361, 6380251, 1072478, 7538910, 6575077, 2299691, 357672, 6059918, 7761728, 2719, 2916725, 3903916, 711006, 1142325, 5487980, 1402978, 4348296, 7498675, 1361252, 6788577, 2013663, 5554585, 2426910, 2087852, 562976, 4283167, 1370205, 3799675, 2456657, 5508792, 6844323, 3160206, 8290459, 1849124, 7783578, 1705642, 7100589, 6784085, 4247287, 1934806, 6630959, 7844971, 3763131, 7277827, 6602672, 4177087, 2143611, 3493464, 793674, 3265316, 110118, 3241791, 5962332, 821315, 641226, 677919, 3160611, 4721079, 8059565, 7002344, 818282, 2829945, 1394081, 7785497, 1822035, 3095172, 6681800, 8070375, 8116877, 4318675, 2268327, 6683145, 363463, 8176146, 517683, 674472, 4465338, 8112234, 368252, 6441190, 5476993, 117273, 833422, 4145821, 2981377, 3646429, 4942671, 2953581, 819001, 8127360, 7464380, 3849563, 5124381, 6326402, 1816121, 1128029, 6312634, 1155416, 2183361, 3524156, 1124628, 7581748, 6929294, 4411460, 4726995, 3765962, 4322374, 8120351, 3695552, 8105266, 8083610, 5517226, 1578032, 4914359, 5527258, 4049156, 4801084, 1714222, 5864758, 6995161, 1654058, 5165759, 7535712, 259080, 563467, 1939936, 7994774, 7193002, 2856710, 6590944, 2338788, 6916463, 2369019, 4076049, 6422223, 1552037, 4796880, 2450700, 3103836, 3939607, 1742095, 1033026, 8005856, 4436813, 2921898, 7169992, 4681291, 7643996, 4674053, 2336273, 6315155, 7272719, 4456335, 7433433, 5860050, 5476622, 6451614, 1854352, 4427131, 6631114, 5225425, 3615943, 1288279, 759227, 91777, 1735378, 33874, 4961088, 32095, 7027260, 7847899, 4606074, 6480389, 4497425, 4440158, 5333828, 1231298, 5800474, 6925753, 7283067, 1214900, 3998968, 3800968, 4144474, 4684301, 6653901, 5732652, 3235856, 4183720, 8242042, 360930, 5704421, 5689570, 2278355, 5318049, 196867, 7131360, 1766897, 2038927, 8243437, 5117414, 6756360],
[6236195, 7431543, 1457893, 8100690, 3729271, 8106701, 5881850, 2312717, 568412, 6973925, 4003919, 3185729, 597396, 3897471, 7735953, 1930914, 4391910, 5951459, 4361046, 313392, 908233, 7667635, 3784333, 3603053, 553364, 6733734, 5636749, 1309855, 1843546, 4300530, 1286211, 5472645, 1552989, 5044949, 5786552, 535108, 7163675, 2900245, 3382266, 5157932, 4669105, 2557890, 8424, 6710468, 5270281, 3691475, 3082562, 3284881, 2178271, 1451547, 5375897, 5658364, 7648359, 218322, 991839, 3673381, 2100265, 1501528, 4736926, 7549873, 6751285, 30365, 4462361, 7657648, 633890, 3147264, 1388580, 7544591, 4244653, 6519485, 2657071, 170273, 5359892, 2707189, 4135658, 2693496, 6174855, 3060675, 6425192, 4024365, 3495922, 4739059, 3068639, 4928352, 4706142, 7253038, 3392229, 6855607, 6515226, 8010373, 4665336, 6579153, 4768005, 392895, 6333513, 5918832, 1113124, 901024, 3314774, 40077, 2038944, 1119757, 4877430, 1853578, 3233818, 555, 73873, 318065, 1960896, 1080021, 2622472, 2313294, 2003931, 7451336, 5311495, 2830497, 2398035, 8116945, 3872691, 2246729, 2437436, 2909235, 3659712, 4290499, 6398513, 1089317, 1554909, 1965035, 439147, 6900082, 3041317, 851387, 3980021, 2017247, 2363513, 874987, 6239323, 277719, 2066158, 3292405, 5212611, 1882004, 8086983, 8142073, 5319210, 489706, 6892263, 1573817, 2619385, 2845722, 5024413, 3711832, 6981549, 908923, 6032731, 4950531, 2118422, 4237040, 7644079, 1633789, 5954192, 8370633, 2907017, 5566607, 4659395, 6118732, 6840812, 1868534, 8238730, 6804768, 4032658, 5024393, 7857475, 5080550, 2895416, 7421612, 1695749, 253389, 4139639, 2438614, 2872645, 2669373, 1290961, 7888303, 2116931, 4518818, 1573158, 599, 3142471, 4619457, 1570462, 436457, 6905198, 2229516, 1946146, 5698275, 2136326, 6886720, 1110048, 3354710, 3539350, 1503417, 3012098, 7404425, 108397, 6011659, 2896412, 8183674, 5520462, 3657990, 2114073, 2713659, 6222415, 8054620, 3841470, 3244809, 1589834, 2459431, 3556047, 5194939, 1693985, 4474140, 7512620, 6369307, 6331202, 6236032, 3306436, 4878875, 994236, 4824136, 6685968, 6500460, 6067862, 909883, 7409715, 3766879, 3201989, 1703167, 7535423, 5119796, 1378583, 5068609, 7426595, 3828924, 6654022, 8307091, 1558886, 5625783, 7220155, 7563745, 6835869, 5545399, 48390, 6524038, 7414573, 4126936],
[6741552, 5514206, 3147992, 2211582, 6634065, 416486, 5799592, 4424550, 298775, 35766, 3342080, 4386467, 1431022, 5947835, 4595354, 3617540, 496744, 7819525, 7997227, 2788981, 1505392, 4281905, 6913620, 771438, 8138929, 2676344, 4845439, 7489097, 656773, 7596304, 7016403, 6835373, 1787639, 169249, 2897003, 3303288, 7276276, 640984, 3603968, 3515383, 2516757, 307909, 553655, 8159148, 7403267, 2844338, 1321477, 3704776, 5837883, 3580977, 7410828, 2934814, 4649644, 7910796, 3395283, 7434293, 3886747, 2341467, 3212262, 6392344, 2810572, 5659501, 1103997, 5288302, 3352415, 5886168, 1414923, 1168750, 1305812, 637664, 3913686, 5493274, 2698136, 4638453, 6971904, 7034786, 2353784, 168770, 155684, 1423764, 2925873, 4662644, 831119, 2431934, 482955, 3453844, 8171049, 809306, 406678, 7641180, 3608438, 3242264, 1761423, 135855, 4634575, 7752859, 160873, 2303417, 2594529, 7450278, 3825887, 3133939, 5976641, 143382, 7327504, 5028123, 6768980, 4239332, 5767570, 8259802, 7637946, 58598, 7577549, 6410440, 6693129, 988002, 584659, 4338536, 1138597, 4518317, 5297890, 7350655, 3404583, 4057226, 7268066, 4511484, 6611193, 4269050, 2287173, 3358585, 1040123, 2629126, 7785456, 4614760, 3783414, 1857004, 2988627, 2326977, 4457784, 4252697, 6896791, 6873893, 1685832, 612505, 6607773, 7798773, 3563997, 5142693, 869498, 7644349, 564065, 4422102, 609652, 8062989, 6097415, 4337738, 4713792, 4397661, 624298, 411636, 1513854, 1327928, 1388733, 3573211, 3488663, 7204030, 7461586, 4965381, 5162634, 4162725, 6380292, 5453737, 2864204, 3248690, 1585301, 2741652, 3045072, 2364450, 1446037, 320009, 3722270, 8004097, 6691002, 4149824, 339468, 1277144, 5469765, 7095671, 7903732, 7394246, 76790, 7235974, 7666900, 1504095, 6114532, 6257083, 1827174, 2776241, 2353419, 8322837, 5285458, 4260523, 4679271, 6291339, 7912946, 4193237, 131299, 8196707, 1313633, 631285, 2152850, 2452937, 1811793, 8131913, 4896793, 648310, 3680312, 2115260, 6152936, 7368743, 6179432, 4565948, 3399981, 5106380, 36510, 668989, 2535270, 4135684, 467277, 6106767, 6190890, 7792816, 62288, 2885981, 7888965, 5214484, 5650871, 831202, 6410542, 5554335, 1696037, 7744392, 5347427, 5909749, 2179597, 6960489, 5045896, 3451923, 1249141, 6723107, 3153271, 1853685, 7642491, 3599058, 1508352, 1587213],
[152114, 2214903, 5194789, 3784620, 4050224, 3256336, 221853, 5478604, 3871087, 1509069, 4981976, 6860938, 5289137, 6198347, 7403770, 2868886, 748029, 3147553, 8170854, 3261341, 4793607, 1666562, 5262650, 1820034, 2469365, 7719751, 6534725, 489374, 44543, 7764881, 4401149, 1363680, 3361706, 6351951, 2342251, 3023993, 6512508, 426293, 5517042, 6892908, 5128878, 7439047, 8125554, 5841619, 5444227, 5517379, 5060757, 2859386, 4917218, 6498532, 986589, 7007622, 5603099, 5471979, 7361654, 5451143, 2848603, 7213621, 4535555, 6941945, 5725748, 4722374, 1133101, 2634647, 6781148, 8262970, 7982575, 3516164, 2822127, 882625, 7367141, 5008526, 857092, 5284495, 7087232, 1642890, 5314218, 2990821, 2360176, 3059904, 5601185, 6724041, 2575920, 3580505, 4838672, 4236692, 1052119, 1186453, 7500538, 7958698, 2781722, 2915679, 3980853, 1247201, 5188414, 3382391, 5615055, 6499582, 4150090, 2943721, 1824963, 2523885, 2132891, 5965980, 1388904, 2958176, 5554774, 7828135, 2960772, 5067646, 4974938, 5434267, 5443125, 7897712, 5436036, 5898899, 5671323, 3505247, 362933, 6485536, 5100697, 1851743, 3610262, 1457633, 795503, 2991930, 2910238, 3876542, 4549047, 1448955, 6478023, 4563962, 4452252, 7179898, 5783900, 5138646, 6099473, 6237592, 520890, 1347313, 6437475, 6352020, 3216475, 3682880, 4683300, 7117026, 2923373, 4430939, 7496944, 5622976, 3213314, 3475950, 5854609, 2378194, 5485904, 4942298, 114678, 2734358, 2826801, 7202857, 4815575, 3273014, 7520420, 3126772, 680976, 48440, 3379477, 1320632, 4171609, 3991226, 8117536, 7470841, 5431565, 7290051, 6308529, 7622332, 1560656, 1765154, 1671309, 2335241, 1747154, 2603083, 2914077, 182952, 8247319, 2230828, 4827005, 5496887, 6119273, 5437829, 6536314, 6764939, 4871053, 4502090, 1497575, 2764538, 3351376, 6212496, 8244516, 4227050, 6760098, 1039645, 1963268, 3758501, 7798756, 4469859, 3038854, 3716108, 7926555, 4034396, 4118631, 2567202, 1538231, 8377310, 7559099, 3763652, 196914, 4665246, 5898591, 1349899, 1366657, 2030500, 2478115, 2937510, 8213891, 1192721, 8294702, 7629827, 2253835, 8280176, 114583, 5548057, 7305486, 5318127, 7060099, 4411343, 1269190, 3820424, 4246291, 7785200, 3386118, 3377071, 2622697, 8376151, 2060001, 77343, 7972656, 4059936, 2115502, 300263, 7897894, 7403934, 2654499, 2107787, 198425, 4682165],
[847441, 1112508, 5214273, 5712697, 1098878, 5421537, 5446584, 3698521, 7690566, 3829976, 4034642, 2760430, 7884336, 8168784, 7271536, 2201634, 8053845, 6251401, 2196870, 1159864, 5380695, 4258164, 7759252, 5990234, 8362466, 3000640, 2946643, 1351999, 7727481, 6609715, 4824329, 7825333, 7120516, 1282728, 5745334, 5563203, 3068049, 3091175, 5326475, 6343761, 3762198, 6997353, 908179, 1793342, 7977714, 2306172, 5511183, 6757789, 3892404, 1694081, 1058257, 7493238, 4785775, 6333345, 4859416, 6925434, 3402860, 7314839, 6976465, 2498707, 273459, 1692319, 1441275, 6124665, 7118845, 7601741, 2194861, 1864507, 8125645, 8379083, 5609959, 2128857, 3305123, 2175987, 3988656, 647978, 2875466, 3562303, 4941983, 733873, 6577817, 1977419, 1110825, 3856486, 1991089, 2248055, 7492661, 497254, 3302301, 244249, 799684, 3563120, 1909559, 5984676, 1599326, 4609508, 846504, 1399565, 5942152, 4990231, 338200, 6660654, 317501, 4464900, 7633013, 1478918, 259970, 6005231, 962514, 4221805, 6292404, 502072, 5485715, 5699212, 2803861, 1790766, 1739682, 6696008, 5940002, 1826330, 6601902, 2536308, 2300424, 5831673, 1226909, 2781640, 2869174, 3585759, 4403722, 2637476, 5481787, 4666610, 5183636, 989550, 3701937, 5950044, 4430445, 8052666, 7470833, 4380609, 5792855, 645783, 7998577, 7892458, 1097511, 1382569, 3916596, 5131467, 54853, 364241, 1230870, 1298065, 5289466, 3189726, 5741559, 5865735, 3985450, 5916671, 2668466, 5361938, 3101333, 3573081, 1625894, 1008380, 3346722, 6733010, 6175633, 1562486, 658709, 888902, 1482942, 7308668, 8226852, 6819912, 4277543, 6728011, 6797029, 1976522, 6856406, 2251021, 2692727, 7553549, 2492860, 4906022, 2011698, 6355644, 7473386, 4104674, 796180, 4121308, 4163803, 457129, 417543, 4661054, 4789029, 6764971, 4662554, 2717942, 6898760, 5824081, 2236949, 1276861, 5437542, 2895319, 5870740, 6664779, 4639537, 1910826, 5518169, 4867461, 5045440, 7819462, 847119, 4013479, 1990026, 3466835, 8179487, 799826, 8177691, 794895, 497262, 6503506, 5718439, 6163811, 3069409, 2676560, 1824232, 730342, 6550671, 126684, 2682296, 2996403, 5928466, 1019407, 381692, 5231174, 5018052, 667841, 4223090, 7522191, 3157450, 1749409, 4393306, 7207703, 650104, 4513150, 2288258, 2537867, 1683861, 7432701, 2540434, 4830782, 3979641, 64946, 5028240, 225331]]
aHat * NTT(z): [[1921421, 4549867, 4572561, 1346644, 5539201, 4193813, 6396665, 2367024, 7514888, 6357899, 2904798, 3076149, 1746584, 5854014, 20922, 3451673, 7051577, 7528886, 140308, 6142706, 2559681, 6072444, 402296, 4328574, 3098081, 835552, 4278663, 6567497, 5463153, 2979081, 5608742, 7160450, 8082368, 5969425, 5861442, 1060519, 4072784, 4987523, 2098217, 6814527, 5364818, 4690732, 345736, 1485338, 5431692, 7337934, 261324, 2378855, 958943, 982476, 157792, 8220009, 2135934, 3233003, 8312124, 5157883, 5026173, 250914, 61524, 701048, 3472724, 355382, 5762276, 2102143, 3348110, 1964196, 4646438, 8013904, 7332791, 3149513, 1194180, 7238024, 6435771, 5936372, 2467354, 2885402, 3121654, 7600901, 1211138, 6282126, 2977398, 7028639, 812232, 6983869, 2077797, 5519453, 7911481, 3350687, 3931163, 6702852, 6186519, 4006207, 2719557, 4217212, 2179661, 6265630, 581499, 502606, 2723894, 6873920, 6704712, 5739576, 6936288, 1945832, 4843596, 6807347, 7949910, 672272, 2691597, 8039211, 1983677, 2714692, 7474629, 7643401, 3731149, 4804731, 5145765, 2493782, 4902767, 7988645, 5639750, 5847499, 4498778, 3761819, 6053686, 5210491, 3843329, 6595276, 8346016, 2010365, 8054459, 6791174, 640683, 4188545, 3274702, 1956999, 2238420, 815950, 4841979, 4339070, 2617016, 8195438, 4819118, 3459402, 2780389, 3354566, 6311927, 4351921, 5743035, 5876728, 808506, 6800473, 5989957, 4474308, 1274414, 2052273, 2706261, 466481, 6524309, 7657751, 7241934, 3917377, 1339186, 4588548, 75003, 7817269, 390402, 6280184, 2067334, 8102458, 5682956, 3944665, 1386554, 2933703, 1418026, 3589197, 3004327, 7282757, 7735695, 2643135, 1949212, 3303199, 4221695, 5081073, 5160256, 6417424, 3413253, 4828093, 4307068, 7734289, 1871072, 7551456, 4888520, 7476328, 2757796, 3464752, 4254833, 2158926, 4960445, 7244685, 7798142, 4424226, 8301193, 3110785, 2937711, 7385119, 6226017, 3230458, 826209, 3399266, 6882732, 7859507, 1815255, 5419863, 413752, 7891538, 1778916, 1503379, 1384527, 1531093, 2766579, 147639, 690471, 2921473, 484696, 1780583, 1844929, 8044053, 5125259, 6433353, 1555732, 7016271, 7554443, 4208778, 881301, 5781032, 1333252, 3564186, 1549393, 2186853, 4431253, 440113, 6574103, 7865002, 1343267, 4767437, 5070957, 5260964, 194139, 7789439, 2147022, 594415, 5949982, 4798585, 4584341, 7671333],
[5808379, 3769867, 4323172, 1981885, 6898546, 5213668, 5250477, 4775505, 8037473, 1269239, 3951516, 1847605, 507604, 4153686, 6830046, 6086641, 3180929, 4126299, 3379266, 7698286, 2581846, 2508116, 4193265, 2465000, 3512669, 6092642, 8132748, 5155130, 7606584, 5418202, 1982434, 3320163, 5428999, 6829137, 6767206, 6772045, 1502137, 8215207, 3578444, 6602755, 3408242, 4513700, 5461165, 1589883, 4828323, 7610603, 2391924, 4024924, 7083823, 4487656, 4479740, 1769157, 4012812, 3138769, 7893197, 1626519, 1103297, 1965576, 3966775, 1711388, 5348371, 7564610, 6987936, 4975077, 3085161, 6219776, 3602596, 7982094, 5362917, 1946014, 149056, 3758596, 1643747, 4695343, 7466598, 2571402, 7772819, 7036861, 5893632, 4207625, 6725486, 4977803, 3786221, 8190818, 7865542, 5898130, 7017325, 2457270, 4591368, 2006720, 3861677, 8327692, 3158154, 936274, 7788066, 1299880, 1668230, 4313349, 2735729, 4090121, 1026473, 7725053, 7625378, 8261376, 734187, 6729344, 169941, 6652808, 1667931, 6830489, 3997963, 396643, 7053660, 6992819, 4287583, 4531107, 1287760, 6128455, 1378633, 7772725, 8353157, 3366419, 6558142, 814434, 2187714, 2074950, 6734156, 1178083, 4969220, 6480704, 5584255, 2155125, 313605, 2448143, 1298607, 1101597, 3582896, 1274298, 4688794, 134791, 2702410, 1121717, 2428476, 4597045, 1610746, 3298865, 6482154, 8084265, 6566162, 1799393, 5993849, 3817047, 726963, 8136955, 7625081, 473129, 740643, 3719077, 8152480, 8122354, 5893170, 7420445, 99075, 1332450, 4284957, 3370117, 7541101, 1518361, 1531494, 5238898, 2376098, 92618, 7543847, 5921384, 6451536, 3753247, 4471702, 6053271, 4947246, 8048290, 4884038, 2730378, 553689, 1433596, 8162377, 5746937, 7450264, 2289873, 3616092, 7545668, 4205676, 144993, 4178853, 4018803, 5441570, 6665618, 7716199, 2883514, 7857690, 7139766, 3699135, 6507479, 881352, 4347041, 4748682, 5397901, 6083263, 7579522, 6427267, 502787, 7371269, 2341979, 6727649, 3231640, 5958324, 4563487, 1157247, 2716422, 1418882, 466010, 308875, 3234765, 4426652, 8158647, 179324, 6398246, 1854468, 5627192, 2067898, 6182705, 490788, 1824714, 6229145, 4877837, 3824451, 6756532, 7709338, 5049605, 4822849, 7988818, 5995907, 5163229, 5457858, 6361441, 6776739, 4466338, 6179884, 3332377, 1404879, 7432434, 1038712, 6817581, 3634732, 6843366, 6834093, 7522635],
[3389016, 6045450, 1174858, 5715429, 6336124, 3043074, 70683, 3127896, 2617947, 449219, 2735576, 1171378, 6906726, 5207722, 1485521, 1350590, 5272361, 3986744, 930754, 761569, 3251968, 2042939, 2845622, 4290837, 1747377, 7039167, 3898995, 4748521, 7304312, 6250523, 5947442, 6608058, 1392946, 905762, 8088318, 7849817, 3848715, 6441054, 7984769, 1561740, 6491356, 2972610, 2294052, 2853926, 2060967, 3239627, 8107771, 4111573, 792919, 207748, 6907108, 1983220, 5980006, 1203356, 6956714, 1786435, 4343846, 7761917, 655011, 6887035, 1407582, 5511406, 3268265, 8272795, 3876196, 2889687, 7106753, 3021460, 406477, 3560677, 1480955, 6968628, 7956680, 5464746, 4435297, 7603207, 1510975, 4423194, 5055457, 7651339, 4198597, 5063919, 3369930, 8002095, 4789203, 1207850, 7643769, 2959548, 1409443, 6482317, 4340320, 2028403, 845953, 535715, 5610552, 2556836, 4394994, 4808034, 1139262, 2275041, 6396066, 7039924, 6998427, 6386842, 5451323, 2862983, 7413054, 3662384, 5199793, 7699607, 4493117, 1170878, 1389041, 3524798, 4717846, 1311715, 1279707, 2973960, 6144492, 4044054, 2212940, 1578237, 3298010, 1106008, 5683368, 6980110, 7531215, 1289564, 8099225, 1004693, 5407146, 4217338, 474252, 7534601, 2779335, 4379626, 1063611, 7680387, 83168, 6878731, 7747468, 7158197, 3136229, 2815127, 5976889, 1207219, 3399228, 2085545, 2821732, 3365143, 4867036, 4234306, 1804407, 6623665, 3332279, 5810121, 4618834, 2437669, 616116, 7925618, 3770047, 8228945, 5529956, 2437872, 4108753, 6139847, 724393, 4241267, 1829639, 3104872, 1366978, 3208525, 641241, 7370180, 7936078, 1964182, 6256501, 7547542, 1000016, 232455, 95455, 4570142, 6403173, 5373047, 5213003, 3076541, 1373370, 6402280, 1305747, 2247743, 7473048, 1120922, 425836, 5302859, 189672, 1998319, 4413126, 2601206, 2751528, 2465558, 5405832, 1651407, 3837840, 3505231, 7758552, 7600947, 1508687, 1670360, 7048261, 4304021, 1455088, 6158031, 687080, 5197178, 7974405, 1522969, 1564508, 4572070, 3045720, 7475468, 7977127, 7415060, 3013489, 145860, 3086, 2859455, 5729385, 4018951, 6987498, 2329719, 1650899, 2955697, 4195588, 3733840, 6808867, 4639171, 168098, 652891, 3181467, 6889732, 5891396, 207236, 3929324, 411061, 3752133, 339326, 4113747, 5851446, 8258915, 2416163, 5026933, 7180493, 3448147, 5384861, 3689756, 4582595],
[204560, 735344, 5587246, 959362, 6153771, 728074, 3987579, 1606941, 1203415, 722729, 3021020, 7979599, 7564868, 6483012, 2452714, 1626101, 3750880, 7874765, 996270, 4915085, 4176017, 174107, 6955473, 4495288, 5492007, 362584, 1747426, 2930146, 3402238, 4392158, 6055083, 4758642, 7084099, 2497044, 542545, 3202328, 3035242, 1208391, 7086738, 5020480, 1209855, 2719423, 4456733, 7939386, 4686699, 6418029, 1162726, 1656754, 134800, 6917287, 3394865, 782276, 4256424, 6201573, 658524, 4682891, 1532821, 6864898, 2334798, 4395362, 5754960, 5589367, 977796, 7738649, 5337641, 4535351, 6433880, 3393575, 7390215, 1596802, 861503, 5704381, 6028645, 1275000, 3449903, 5682417, 6502929, 2323109, 7889810, 3233590, 3081223, 4818255, 4578652, 3986825, 6341476, 1650066, 1808173, 2388342, 7892657, 8228497, 5491085, 6924243, 4062396, 2363203, 5061724, 2271216, 7692462, 4379988, 5218502, 3822440, 3145127, 4900134, 2578641, 5493328, 2132113, 2545040, 6030090, 1404515, 3872195, 3168449, 3199662, 3180156, 8181500, 4077736, 8020281, 6951563, 3056939, 6525093, 2524477, 4771061, 7828962, 1363298, 6630208, 6052866, 595407, 4152359, 3459101, 2874698, 5305281, 5274321, 1719917, 4946019, 7226328, 2457861, 1023305, 87038, 4272913, 7848704, 3113356, 7254427, 5861590, 4265193, 5311670, 268404, 4859147, 7738273, 3379532, 4466086, 4936863, 5278959, 1872536, 377035, 1836522, 2003548, 924952, 931240, 1162866, 2943468, 618817, 5110318, 5061440, 400501, 2277191, 4518723, 389235, 7561666, 6136162, 329901, 5047090, 2854993, 5131074, 7141930, 1937239, 5690544, 280290, 2571998, 2836354, 3426321, 4549828, 8244368, 7010141, 3591776, 6990602, 7816134, 6961131, 1072244, 224720, 4145935, 2484797, 7903533, 7036457, 2847231, 689482, 131087, 5543193, 8066198, 8289741, 4632489, 4787781, 6689016, 7336357, 8236356, 2833775, 238664, 3050326, 23136, 5075656, 6506092, 8200135, 3176608, 4661735, 191101, 1181674, 6494521, 4035079, 3968203, 4479067, 4500000, 7497362, 4419644, 1955199, 2035620, 4070831, 5411456, 2477735, 1475305, 5965975, 7821059, 120352, 3608944, 1275507, 6845385, 3585518, 7579652, 2049148, 242146, 472127, 5880369, 4466793, 7434346, 3925162, 6557602, 7313686, 4815212, 4461651, 2632665, 1641302, 1236710, 6759439, 482012, 1037645, 5201043, 3901415, 3953324, 3701452, 5456205],
[5462952, 1043296, 3578626, 1294625, 4856419, 4673395, 5969503, 2503087, 4228667, 743672, 4642468, 4397787, 1467341, 7803633, 7944641, 4211995, 7233503, 4597278, 5164442, 844881, 7138253, 5530576, 3787643, 7666584, 5356114, 2000792, 168153, 5404250, 1182624, 1084782, 5445085, 2322344, 5024620, 465588, 3213403, 6162283, 5448238, 283059, 7643310, 6848381, 4468879, 7775955, 6478347, 2465540, 3714266, 7408531, 2519460, 1279775, 1479813, 5595651, 5938654, 95109, 4241943, 3754453, 7438494, 6390217, 2045216, 2708896, 2517733, 8179307, 7689847, 5654306, 3885027, 5003725, 1316612, 603597, 7137466, 7335154, 5031917, 733439, 1472463, 3709367, 1895188, 1511819, 2851571, 663467, 3330009, 1634454, 4221035, 8068895, 1881401, 5842158, 4967268, 2573389, 1019079, 2920245, 3651959, 4004951, 6435769, 69266, 6099829, 3922770, 5080277, 5773136, 3930303, 7470548, 7126833, 382244, 6925695, 702507, 2349480, 1433943, 7341397, 3481782, 4877417, 8112161, 7406565, 8177507, 5159073, 2668163, 3038294, 5062380, 6973198, 5103666, 1696121, 4860897, 8160649, 1749202, 2275101, 3154765, 4293224, 7859915, 1930311, 3919091, 2986908, 1415439, 772064, 5270487, 11244, 1874643, 807847, 565045, 4650160, 2988834, 1941205, 4904363, 2264453, 4746482, 6129116, 5506223, 7323146, 129901, 4559894, 142521, 4410058, 3189062, 2886103, 6705600, 6638760, 2649688, 4956242, 497939, 1668070, 379980, 563635, 8361395, 2906224, 3728504, 2391793, 669507, 7017441, 3869488, 1439170, 7126426, 7372362, 6396906, 249232, 5174404, 7664934, 709336, 240686, 2504498, 4478867, 750483, 4351548, 8177436, 4235011, 2890185, 3624008, 373791, 631416, 1909231, 1794456, 7763859, 6011846, 2054820, 6833400, 4659406, 5573474, 6861181, 3541292, 4107783, 1155052, 1398827, 3540318, 2301571, 6083803, 4718217, 6910989, 5240607, 8074459, 1517792, 4888111, 1892227, 3371594, 6729967, 972437, 6798502, 4981093, 1742252, 6018024, 159481, 6074633, 4432553, 2373258, 634302, 1971470, 6093679, 7838557, 4448807, 6292068, 1322868, 1183313, 172349, 5979068, 381150, 388750, 3037499, 4246853, 5230697, 7822686, 7733158, 1996539, 6976532, 4291133, 631695, 7893526, 6333903, 4522824, 8244799, 3030729, 6268294, 5780837, 205735, 2558739, 2330047, 685774, 4968184, 5322104, 357030, 5627468, 6296906, 7984327, 3905848, 5491718, 357874],
[5288504, 499627, 4343506, 337774, 1471678, 4252574, 4690653, 1736836, 3682737, 7583299, 2601701, 1037933, 638666, 7767567, 3901022, 1638857, 3805095, 4120147, 4999127, 1632669, 7548907, 2918776, 7500139, 4653899, 6696914, 5334016, 1473696, 2282168, 7471659, 7320070, 1651110, 4503451, 3597806, 2381006, 2029865, 8049697, 958330, 1567194, 7648863, 5035382, 6008679, 6430754, 5360952, 7807464, 2960220, 4562532, 3927026, 7293206, 3265316, 3602315, 1007088, 1986200, 3178257, 5206512, 1473860, 4670922, 5833464, 4025411, 192774, 4211421, 6819128, 204240, 7414369, 4153818, 6890613, 5569303, 4755080, 5814864, 1146508, 611844, 2369514, 5903071, 2131628, 5197798, 5522951, 1101933, 3557879, 2563703, 1418496, 2419862, 3582744, 971238, 7060746, 5299502, 6730900, 480716, 7145298, 2844197, 1634317, 186432, 7314816, 6958047, 3702081, 431530, 3977163, 4405541, 3681903, 549803, 3029689, 6046676, 3191866, 1739820, 5691486, 3708426, 3679526, 414144, 1082904, 6352483, 5483823, 3402661, 6908486, 3500929, 6193276, 2580558, 5275721, 382226, 7060916, 3113322, 2589816, 5163902, 4359874, 6668719, 3099066, 3134180, 5141909, 4070787, 3287983, 4850742, 1529519, 5218251, 8166425, 126464, 1895644, 4048407, 8131220, 4887208, 8223539, 563052, 3585453, 3601668, 577797, 3160863, 7853123, 1647684, 3632294, 4237247, 6409516, 7727688, 6648916, 6210131, 2518766, 5328280, 3249229, 892768, 7585860, 1759442, 4224808, 1965660, 4926164, 485768, 1733379, 2552699, 7016291, 417084, 7195476, 3722244, 5790036, 1150563, 7614775, 4427998, 2844795, 3700917, 2038195, 7762549, 7352049, 437527, 772720, 6502775, 1398878, 6267402, 5257388, 4845156, 588533, 3272451, 5488234, 4519808, 3719919, 6149973, 5461667, 4018273, 1143312, 7703674, 8122159, 414070, 5080192, 2883456, 4455077, 7750240, 2976425, 1865193, 6950372, 2232608, 2816905, 5123792, 1767750, 6654925, 4422394, 7216114, 2108025, 3181187, 2424144, 2802905, 3911366, 4794831, 766799, 5952775, 3325506, 3710751, 4765842, 2980050, 7480002, 2956099, 7545562, 4731180, 2454499, 1324438, 6892522, 2242579, 5462283, 6350207, 6738995, 3840795, 7740498, 973926, 4828353, 3303128, 1847785, 1512419, 3750079, 5591017, 7495234, 3920840, 2631635, 5301978, 4175650, 6793844, 7986988, 2592077, 5378051, 3423808, 7642970, 105629, 5430412, 3579749, 7337121, 2461364]]
NTT(t1): [[2465103, 2822635, 2594302, 2910374, 1036426, 2094292, 618434, 5132084, 8210004, 1708789, 4084084, 5389518, 3845241, 4241152, 1096633, 4931405, 6811198, 1187541, 2493940, 4907330, 2540541, 4855926, 7450141, 5677353, 2141331, 4290553, 1194864, 3258203, 2624409, 7772397, 7291668, 5648877, 4641288, 2097607, 1482031, 5822315, 3562054, 3840902, 1928868, 4883382, 4601327, 7000987, 7247339, 2926730, 551439, 3022367, 1058829, 2715079, 1613054, 4976717, 5451463, 3084519, 7103168, 4027847, 4684692, 6882045, 3432886, 7139447, 6920229, 7077008, 1775903, 1636444, 6746543, 5010599, 578493, 1042930, 1814232, 3764155, 6351121, 7793658, 6953696, 6455464, 7544831, 4182288, 2342867, 2239519, 5820499, 6336676, 7214586, 6797948, 7162193, 6786824, 7471125, 4745380, 7166676, 3190191, 2974815, 7318032, 5364419, 7830175, 728984, 2223545, 6479411, 2551613, 7366355, 2917229, 1787355, 4257600, 7911122, 6458846, 272496, 2895842, 1563332, 4738741, 630128, 2677028, 7360090, 4960604, 6642604, 3348584, 7552848, 7556226, 6995055, 2001871, 6315219, 2760311, 525390, 2124427, 8002195, 3208106, 2030864, 676695, 6078178, 6270505, 3098120, 7411852, 1703069, 3358278, 4683254, 2798507, 7797677, 1424293, 6700691, 6759264, 5298931, 4869753, 6543357, 5742714, 507500, 6193230, 959556, 3048974, 6023896, 2669711, 2715833, 7153611, 5689153, 8308062, 1707578, 5024144, 7718170, 8309608, 3206757, 1432072, 781830, 7384796, 3479713, 5099252, 309708, 5369434, 6341509, 1525091, 8220284, 2521393, 3252951, 63123, 7184341, 5858651, 149170, 5732571, 61842, 5262372, 2384977, 7092043, 230620, 7841635, 2920731, 477260, 1439478, 7355284, 7828553, 8348717, 5617493, 638472, 2371278, 2922110, 2840881, 5546630, 3401537, 345345, 8068376, 2202145, 4857942, 7226326, 1629087, 5185240, 7577959, 5300769, 1445524, 4758323, 6212623, 6966642, 8065316, 3681542, 6635706, 8317961, 6738386, 6613130, 7513372, 7280664, 6453542, 4372651, 7484064, 7477587, 3337036, 3031044, 1026276, 143691, 3639865, 507770, 6422807, 7965295, 4342288, 4368466, 1345950, 1272043, 7384097, 2914668, 548728, 5625749, 4253044, 7000388, 7854240, 3897427, 1817094, 4072302, 5197687, 3906854, 3849422, 7128041, 4458333, 2737935, 1040230, 5657125, 4094833, 2760480, 389530, 3264779, 4762029, 3518246, 6780235, 5851286, 5539344, 2216881, 2376246, 1865118],
[699794, 2800210, 4919939, 160664, 8024568, 4992139, 2026687, 7911503, 6609409, 1101580, 2007299, 380412, 2584548, 5562993, 4010124, 3832417, 7356837, 1326544, 538047, 1177982, 3025914, 751210, 7345704, 5117511, 7977244, 6557990, 1187616, 3765792, 3442206, 1340189, 6766282, 6741937, 1865471, 2593384, 7701675, 8305332, 7041711, 3911985, 7955326, 6727556, 4150463, 3703120, 1169487, 3012574, 3965759, 5397844, 7774176, 1912508, 6599124, 7901817, 2332577, 7119441, 3730492, 8231196, 2562612, 1237719, 1636078, 1212542, 5358500, 4008275, 5229403, 915481, 4865886, 32994, 3163507, 2692844, 8220750, 870059, 3861268, 2529185, 3990492, 5034747, 4153075, 5002347, 4913556, 3139196, 5676684, 1765869, 5829928, 1531962, 2269834, 7196450, 8169017, 4237164, 6809485, 2816776, 6662070, 7716803, 4839372, 1393335, 2820615, 7234857, 5155583, 4365765, 5396960, 7418811, 5605680, 1644277, 6093278, 7794335, 4318830, 3515740, 1402645, 357941, 6209337, 5789189, 5369249, 1272472, 7686903, 114359, 3236731, 3404118, 7494734, 6543368, 7600940, 1792954, 2465533, 6834721, 7410763, 1783369, 4595619, 4715966, 154707, 279632, 1207935, 923641, 3216153, 5412135, 6496107, 210760, 7472789, 2327345, 19370, 3935543, 7701290, 5719550, 3533865, 3648027, 4677564, 456288, 7218379, 4101710, 4345314, 4101258, 3558641, 4885660, 6783341, 1507504, 7160785, 8055370, 2634956, 7484111, 2663268, 3328283, 536778, 2056373, 6190636, 4499415, 5314140, 236765, 2622774, 1869198, 3002023, 5896728, 7169178, 6457327, 2203851, 6151335, 7027042, 2636431, 8217935, 5997336, 5543393, 1462476, 6049623, 1000700, 6107159, 4733671, 5812596, 4505599, 7080256, 3892821, 1368318, 7438106, 8101011, 5909278, 2720225, 2385049, 6401827, 4921896, 7351395, 2198269, 3645059, 5049551, 3240737, 1910347, 8249516, 7444432, 2689084, 6950479, 872966, 4651351, 929574, 796564, 6478958, 4897355, 4354015, 2667439, 8248742, 8319386, 3919612, 5565317, 4864837, 7446783, 4476646, 4887045, 2259065, 1675416, 5195741, 6096177, 3036614, 6357472, 322624, 7333407, 1984147, 7878535, 1551387, 5956261, 8340173, 7755338, 5727584, 7242914, 3441516, 8124994, 7016615, 7957935, 5970699, 5536639, 7791305, 4629267, 2921358, 6546085, 7704635, 611706, 7788768, 5896766, 2308591, 155015, 5591056, 4871223, 7048725, 2615093, 3356678, 1077673, 3584664, 5167993],
[2521997, 3370917, 912088, 4127513, 3520874, 7108176, 400276, 3811249, 383955, 6199522, 3470112, 6573522, 2653874, 7252874, 3635003, 7409391, 4857696, 2490455, 5009560, 3437342, 2807372, 810599, 1089762, 5755749, 467317, 352658, 4539930, 1527038, 7765722, 2450047, 7686613, 7009123, 4492308, 7299073, 8248872, 2208718, 5308280, 8274760, 5680062, 3621075, 1958356, 4032393, 2254756, 1062333, 6067216, 7361232, 5165506, 6639480, 4689286, 1450462, 4248848, 3051201, 303527, 3791284, 6343150, 2604962, 3463190, 6341295, 6907115, 8269373, 3836158, 1023583, 5856370, 5989775, 2199604, 6919058, 8021925, 625411, 213237, 6846480, 5840865, 5860840, 5135369, 1266066, 873248, 4256729, 4731525, 5032743, 2416493, 4597357, 6427220, 6985242, 6606419, 2871154, 120267, 7053593, 295089, 1187510, 4189326, 5635230, 6630033, 6063448, 3695125, 4074593, 4119865, 1349385, 563649, 7603784, 8010493, 7179172, 816828, 3361887, 5383924, 860510, 2817656, 1117889, 1057760, 1989738, 2704211, 5284512, 6984540, 7802507, 7338603, 3948037, 7522807, 3554865, 5766672, 1924643, 8264061, 4347882, 1721126, 308039, 7352717, 3636277, 6561553, 6661432, 6411264, 7684024, 3217052, 756320, 5457372, 7447943, 7174845, 7572015, 5821166, 6176937, 4667965, 3591259, 67838, 7056554, 6015078, 3533644, 3012317, 4499950, 5279248, 3425248, 4825004, 3438211, 5639975, 5336286, 6198919, 702397, 6969478, 538324, 6225786, 4147883, 5313334, 3152940, 6744803, 639270, 2360233, 6700339, 4990079, 6401868, 7327506, 6455453, 3626918, 3428701, 1370394, 6506983, 7691033, 7933859, 3200930, 5185183, 6974711, 5821962, 1017258, 2145232, 3487507, 5752804, 401015, 3148439, 7619793, 2695454, 5643727, 7976781, 1412145, 3367460, 1463186, 6676787, 6353275, 6174450, 557009, 1945305, 4729179, 3124796, 3453114, 7882385, 717654, 1257513, 4336970, 7760808, 6714873, 5113048, 1556272, 3414761, 11836, 1476304, 1474532, 39627, 3555123, 2350732, 1530232, 3521549, 96451, 2879468, 7511453, 5996353, 7465007, 6417949, 2910590, 5589094, 2042198, 4396800, 1127649, 6639449, 4325621, 818654, 5146310, 7163005, 7604302, 4395746, 6878633, 2757996, 7616266, 3336779, 4288607, 7847490, 2312470, 6263, 8316010, 4226096, 537350, 4614512, 6348076, 5479712, 5006039, 2364876, 1917667, 1625224, 4871504, 236610, 1412405, 2862770, 333247, 3152664],
[5656882, 1546516, 6684076, 6736632, 2388573, 4302206, 6273344, 484690, 4004921, 1850729, 7854628, 2634196, 5752042, 1993361, 2803706, 1867998, 268288, 3288181, 4222426, 2361560, 4057123, 2562782, 3262591, 3951155, 1345207, 7269799, 825737, 5712882, 7340660, 8374864, 7677583, 7552123, 5455298, 619173, 8157193, 630442, 2276833, 915093, 8355742, 8362957, 7848712, 1347960, 2435688, 3620434, 5239527, 5132313, 771334, 4562045, 1940551, 2703796, 3475373, 4724177, 8257320, 1535055, 896792, 6619367, 8371623, 3015442, 1967302, 736885, 5127196, 1088021, 825578, 6276201, 4842227, 7043053, 840150, 1707067, 7167603, 969631, 2120190, 5892610, 7765107, 3345992, 636045, 463148, 6822698, 240903, 652014, 3538190, 822057, 3211335, 6880908, 4335711, 2699422, 1553692, 2233019, 3591311, 1060889, 2503231, 7960536, 7274138, 4920652, 2958390, 3275982, 2883454, 2321943, 6665265, 803914, 609652, 6004694, 2634190, 4767898, 5802020, 8296899, 6989028, 6888021, 2820324, 3060705, 2673532, 1329748, 4296433, 5615976, 2983663, 7996727, 6332142, 5758112, 1985095, 4318242, 3819420, 2663796, 7563912, 1454724, 813333, 4044355, 1672926, 427008, 2336078, 178592, 5484674, 601489, 3399933, 2506331, 574269, 2664357, 8133627, 768599, 5635506, 5002954, 5944846, 522795, 1887209, 56080, 2334943, 6658685, 8264071, 6662523, 3940415, 4123067, 6956355, 4478172, 529700, 3886328, 5736414, 2476510, 2400611, 3243593, 6953665, 3938466, 1349061, 6199103, 3887870, 7605763, 8365003, 899546, 5375249, 5722618, 6600156, 6765287, 3854154, 5044594, 6895789, 3968152, 3423979, 4735633, 3904425, 4762046, 3467728, 3341925, 5263470, 6652830, 4779801, 8077841, 3203536, 4799440, 7765892, 4004306, 7498229, 7519690, 3649357, 5433454, 7184019, 8373920, 287002, 2058366, 7110738, 4856755, 5048610, 6340885, 7054226, 5381519, 3303112, 2618690, 4644214, 8020545, 2808404, 282802, 5177082, 5080139, 8035367, 4671059, 2829418, 6052399, 8300342, 8193220, 7980694, 7905382, 4364061, 1865535, 8203074, 4584814, 6757245, 367074, 2319215, 3241074, 8267549, 6186874, 3650486, 4162839, 4715732, 8116511, 1023418, 1808378, 4171468, 638638, 1102695, 2358653, 5488846, 5000238, 5700038, 5172551, 3380099, 2233556, 5478157, 3865393, 7018839, 2575466, 22162, 6700855, 3549806, 5782172, 5802877, 611904, 4093417, 2808869, 5054593],
[5530332, 6656075, 2985085, 6425099, 5562827, 211989, 8111958, 4437937, 3433823, 6261319, 1485321, 6383811, 6089975, 7117748, 7060790, 5508289, 7190185, 6565558, 3076403, 954382, 5753268, 6339866, 4096172, 2781053, 2950010, 2377265, 569998, 1339333, 7497980, 5094837, 7655047, 3032659, 27582, 5297451, 455522, 4801861, 7379179, 7552979, 7586379, 7113717, 6325753, 3503450, 4011703, 5957161, 4686526, 7363743, 4048920, 557922, 4616548, 6808382, 498089, 657577, 5220151, 1641977, 31368, 5620335, 6558771, 589338, 2943246, 4537587, 4170530, 1998200, 6128707, 3286285, 6213454, 6560935, 7636692, 327437, 7591440, 7010590, 1994352, 5801622, 8041609, 7902493, 2866872, 1667388, 1706525, 571872, 197825, 5214079, 1423781, 7464114, 1806487, 5861013, 3013439, 8374536, 4705605, 4099992, 7026676, 91148, 4768456, 3672408, 3155411, 8314476, 7101633, 3391789, 1481008, 7291972, 6290285, 4266778, 4089707, 8334508, 4046751, 7449522, 2074752, 3911418, 5872688, 1388108, 4347790, 3753980, 1047109, 157563, 1676714, 1011117, 1151246, 4114859, 4106847, 6637911, 5438811, 1684428, 4635569, 2736476, 1469526, 3984852, 2318252, 8040253, 6712530, 4236613, 551295, 7832067, 1313966, 4989957, 6904024, 4557819, 7596729, 5250121, 6583940, 5041638, 6319648, 5312781, 2766288, 8136138, 5605528, 4716037, 1169400, 4443127, 3558772, 303423, 6830943, 3301198, 8189444, 7243342, 718820, 6298501, 6380511, 7380609, 4554794, 2828292, 3520237, 2320499, 57763, 1423211, 5846926, 3935371, 6597374, 6475312, 6550063, 6801386, 6333221, 6325267, 1567836, 7005641, 2376287, 5931706, 5355363, 6275036, 6488488, 1450773, 4762546, 3569674, 3285451, 313352, 8054832, 2702227, 2156289, 2333003, 200670, 5527117, 4056455, 1054116, 6267802, 2130280, 8157391, 7650345, 5397182, 5706547, 6069758, 5355618, 6482889, 162634, 1207038, 7135331, 6398446, 2959151, 5453548, 2319493, 3686911, 3003519, 7686791, 70578, 4207897, 207047, 4256553, 2291852, 6786142, 5768767, 7115064, 1613051, 3691659, 5311885, 3597109, 1694367, 7191422, 5267947, 7431104, 3506698, 3232692, 3440571, 8141132, 3367600, 8211231, 6515795, 7668910, 6027174, 7770237, 6996794, 2000179, 2524778, 1547181, 6473957, 1616269, 7002238, 6460041, 7159237, 1696155, 5205285, 876136, 1779666, 282086, 1013538, 5831896, 6145377, 8215099, 4246741, 8195369, 5729575],
[5963162, 5701763, 6163110, 8064739, 4804876, 4204734, 134920, 4002931, 549865, 2435200, 3578943, 5852619, 5102513, 2525367, 1952080, 7897081, 2828708, 6576433, 7794187, 2339082, 1615166, 3674745, 4360228, 3875937, 7986986, 1742553, 7131935, 581941, 1724125, 1288386, 659, 8130506, 3501623, 119775, 1633477, 7998280, 2926304, 6815464, 302222, 3585489, 5703237, 8308945, 3933285, 5787325, 5073992, 2281678, 7772495, 7348805, 1180249, 906476, 6534810, 6941758, 1338331, 1799462, 2886590, 6119686, 7403327, 3835762, 6508316, 6494400, 2625208, 3825097, 4737063, 5448968, 1948111, 4020652, 5445346, 216707, 6626092, 3622381, 664390, 5517270, 6492651, 454421, 1334328, 6784239, 997773, 1590507, 6927179, 1360413, 1793334, 3605038, 2224576, 6812092, 494591, 4409534, 3227074, 8096208, 7187822, 5455571, 7736845, 2717984, 453302, 4783573, 6915021, 3655651, 5708719, 2280412, 6426420, 7502522, 4192688, 4876799, 7315808, 1497718, 4195508, 1253808, 3574820, 6354055, 7470243, 4269035, 3607547, 8277164, 5598432, 6944489, 2777815, 6414652, 6311422, 2821703, 7883247, 4204426, 1561122, 1660760, 6598198, 1943695, 3760224, 42203, 875511, 6217844, 8329208, 722523, 3278755, 3099237, 6791053, 5801059, 1463478, 4994371, 6787400, 7111166, 2925247, 3988852, 6981638, 598465, 3448954, 600750, 5507658, 2565371, 5602143, 1966699, 5443082, 3338927, 7615728, 4206790, 5723474, 7881573, 1613901, 1753109, 4507331, 2361806, 4839642, 4719201, 5726954, 4625065, 8080577, 6186843, 871259, 7063791, 3927879, 6453773, 4103056, 2508618, 2448705, 6662443, 1717628, 7726937, 3141825, 3936773, 4319693, 4615508, 3842488, 4282003, 3931231, 5168789, 7641387, 623956, 1799841, 4901016, 3405720, 5463139, 1023159, 6256328, 3018211, 5664331, 7452483, 1503011, 4160288, 1255744, 8144043, 6568356, 2850367, 3805916, 1162447, 1660212, 2307528, 1040250, 2963164, 6054424, 2473204, 2717764, 8074390, 7884116, 2149769, 5803428, 8258696, 7239487, 1009747, 2125599, 3819518, 3629786, 4029308, 3444918, 6787020, 7416657, 162834, 3134579, 4569636, 6054726, 3737448, 4107907, 903076, 3955876, 5302491, 5535040, 640808, 7729042, 859112, 7861201, 6070387, 556930, 8334558, 5633950, 5126928, 4094150, 4459226, 6723073, 1063250, 719137, 586238, 5918024, 7324066, 2219801, 8220967, 926795, 7764031, 6695111, 2951606, 4005233]]
NTT(t1) * 2^d: [[5699223, 1455417, 8164889, 7877860, 1039371, 1726465, 4439460, 5860456, 3506343, 3103098, 2191464, 2894700, 6607186, 6688719, 8190929, 4459820, 517630, 7052152, 7280251, 8367428, 3536461, 6286710, 5358478, 5941843, 1570771, 741278, 8379249, 7951248, 3388923, 5448275, 6112297, 7318127, 7859784, 3741694, 5954136, 3451333, 8114791, 4583766, 4200611, 4935003, 7335535, 4891973, 3327060, 7779540, 343525, 3478646, 195573, 300450, 6601176, 6917376, 7523120, 1422393, 3917025, 2420895, 3067421, 2647481, 5903077, 7799998, 5375380, 7505147, 8173881, 5462465, 7210558, 7924959, 4079051, 4037637, 3709203, 4403617, 2754496, 3629630, 2983283, 2729818, 1680177, 2158600, 1611534, 1406835, 5335495, 1746894, 3187828, 919051, 1385639, 1975830, 1270649, 5778914, 4588707, 3904466, 7812261, 4195343, 6794117, 1081882, 4980024, 4634499, 6154051, 2053698, 6177760, 5371101, 1423661, 7344063, 2146763, 5293911, 3096310, 6157554, 1538568, 1674728, 8052121, 7042504, 5137382, 625935, 2164387, 2495287, 312105, 2843430, 6579531, 7231580, 1959907, 2102646, 4840959, 5560292, 2359666, 8197057, 1710143, 4029803, 4376779, 4401167, 3896364, 1770419, 6527360, 6484782, 8048159, 4928849, 3031610, 2267792, 329322, 2475569, 6663109, 2231656, 2033412, 5032467, 753168, 8276059, 8232023, 3552348, 3860736, 5764559, 6477218, 6505648, 2042439, 2277447, 1563003, 1559761, 5382792, 6561862, 5526466, 7330441, 2112772, 6398926, 4010679, 5074056, 6242002, 5974912, 7817162, 6724142, 3915933, 5903968, 6828949, 5898179, 6833298, 7801250, 6840175, 5745181, 3784644, 486376, 2979557, 4965612, 3645215, 2777615, 537817, 4439598, 957057, 7668715, 4555292, 106527, 1632909, 982416, 8083187, 3454168, 79143, 7752403, 504579, 4865711, 8167730, 5314456, 6040948, 7177321, 3856840, 5532724, 4891409, 4959171, 203387, 2862549, 7915592, 91494, 8241461, 6451698, 4318890, 7946302, 7431750, 3745472, 3760976, 8152116, 3745628, 2854734, 6701933, 3924851, 78658, 7517294, 1694741, 3858292, 250394, 2965008, 3377018, 1769878, 5533548, 2092882, 5774045, 3717925, 672718, 1152223, 3276264, 2222725, 3542979, 8365382, 5472771, 6713631, 2013456, 6238324, 6933544, 135445, 7336270, 6546633, 806650, 3167628, 7060488, 7842407, 6443102, 3487094, 6471300, 3158921, 8080850, 1217169, 6661661, 6130089, 6728410, 325513, 6878958, 1546465],
[507220, 2118991, 2714935, 434019, 1270108, 7548145, 1013827, 5267915, 6784708, 6814668, 1415254, 7200397, 3683874, 7711427, 8081585, 2117982, 3630057, 6028016, 7962099, 4168577, 7394419, 2686242, 4613108, 3804278, 7471499, 4581110, 7666552, 1053087, 6828764, 482018, 1304106, 2999874, 4438241, 644633, 4342424, 5054538, 3286301, 266512, 3908000, 2516560, 1241127, 7229917, 1620873, 7058560, 5001436, 4057956, 3261009, 4266163, 6334158, 1343956, 1120024, 3138769, 5190082, 1122450, 8353336, 7469895, 2464193, 2349919, 207754, 1314994, 6958089, 7527554, 4074860, 2113504, 3199980, 2520504, 7733405, 4168878, 3813698, 2692696, 6484164, 4615367, 5877797, 7367911, 707901, 5174276, 461395, 1399106, 7154110, 4348455, 6715222, 5465222, 2957519, 7540691, 3245568, 3740991, 2401936, 2564745, 4763014, 72366, 1668411, 1639520, 5614673, 5107541, 5196645, 115628, 5425817, 2587065, 2369724, 795197, 6115203, 5829268, 916133, 7487139, 6137931, 256485, 4459392, 7232293, 656038, 6602641, 8041381, 4887297, 1925986, 2123524, 402170, 5388584, 841366, 468455, 1229748, 2292017, 2477684, 7851519, 1916777, 2891503, 6511460, 7330938, 7074745, 3803990, 460594, 180018, 6521720, 161565, 7831534, 504057, 1188504, 8022570, 3461762, 70162, 3337764, 245314, 738416, 4116567, 5181289, 413783, 5296746, 6835545, 6964762, 5118527, 6612137, 2187582, 5985777, 7086957, 3266005, 3797835, 5946868, 1169446, 3786845, 2133714, 5548982, 3702553, 6755837, 1448157, 4428938, 1272188, 8324257, 1230680, 2529174, 288899, 443691, 1308143, 1433759, 4172058, 6376150, 4987499, 5105895, 1686574, 7137455, 2043373, 7637455, 2510540, 591095, 2502947, 4643527, 7332762, 7340306, 3516784, 554397, 3569381, 7497615, 1985845, 951278, 7083932, 897557, 183480, 7336865, 3324085, 352384, 492435, 5240252, 1770870, 2841771, 6491710, 5651572, 5487862, 2443075, 2075981, 1036128, 3913169, 2392193, 2859068, 4083977, 1608384, 3861869, 2990993, 8359657, 1420631, 2299744, 6265243, 7752746, 977081, 2864232, 4499386, 3104453, 4441088, 4503661, 3367403, 4250132, 2902338, 5537832, 8168036, 6793762, 599128, 1176284, 2679034, 7210294, 139677, 3852596, 1329884, 1114688, 1568339, 5674201, 7620354, 3449493, 7986603, 5472835, 1583484, 5756720, 4439913, 2951847, 5893479, 2082070, 2496004, 1757999, 3718115, 586320, 6712389],
[2471519, 1078049, 4873349, 5984318, 5984911, 3040476, 2317945, 4698483, 2702985, 1157204, 783040, 6112999, 1734110, 6767695, 2322975, 6751158, 4025716, 3872382, 7793888, 504544, 2127176, 3136744, 2186199, 2869766, 6790712, 6110888, 7196331, 5913132, 1049177, 8066726, 6660775, 4498749, 2576089, 8111138, 3457153, 497553, 7826364, 6021224, 2992720, 5550637, 2734214, 6140059, 522084, 3759090, 6760662, 6112229, 3099719, 1713830, 7179801, 7133815, 2691015, 5035098, 5889752, 373126, 4499400, 3307022, 2740935, 6064074, 6890913, 3793005, 7623003, 4774936, 5876132, 895265, 1259418, 4162965, 4759903, 2932125, 3710768, 4613596, 4565427, 592287, 7629925, 5036843, 5151915, 208831, 1224175, 4959433, 1365702, 8334963, 6006646, 1615188, 7431879, 5043466, 4718475, 58641, 3808992, 6798200, 1150977, 4467324, 8128176, 1034457, 397796, 8245362, 1994821, 391897, 8183258, 6939384, 3293546, 6390935, 3882210, 2528042, 7351154, 1367223, 2569534, 6331324, 8199159, 22631, 3454381, 5868499, 4244821, 696885, 5104635, 2289901, 5628743, 7885422, 166395, 3111079, 2179186, 1077094, 3602798, 949971, 3400685, 4379166, 247538, 5555857, 1001349, 2212521, 6058936, 2645277, 5647146, 4113296, 4465819, 6480663, 2419142, 510058, 126509, 4330058, 2621374, 7554319, 7047433, 1651330, 4953216, 6516434, 4647896, 1995500, 4386196, 7623392, 1436279, 2599840, 4597845, 5070162, 6563172, 1850866, 6801467, 5247018, 7326647, 439286, 1336895, 7519632, 1406717, 5826155, 7433459, 7833487, 6382598, 2639706, 3133991, 5141225, 4889285, 5752616, 967330, 4039093, 8074184, 5065780, 7529823, 559557, 3243038, 6095, 815791, 3885577, 8371833, 5469179, 3998440, 7140790, 7031412, 3678603, 3316380, 6279973, 2423402, 5637762, 3639230, 5277805, 4070880, 4765843, 7146994, 4535314, 4002513, 1384935, 4349251, 2014003, 3870577, 2695774, 7562845, 765050, 2365967, 8270583, 4775925, 940637, 3185247, 6168538, 1618541, 7378695, 6937129, 3134094, 2367394, 6108418, 4801362, 4499739, 1434495, 5482367, 1266915, 3639977, 2373684, 7933751, 2481074, 1459878, 3084156, 2079968, 5074010, 8037543, 2802423, 7679800, 8218045, 8279417, 246507, 6353731, 1560480, 459273, 4011820, 1023994, 344127, 675805, 2252275, 6401634, 2951107, 4287252, 4091107, 5920505, 4626606, 5732812, 8195431, 2432793, 5446300, 3405074, 6323899, 6558711],
[5851751, 6248985, 6686331, 1443399, 7296738, 4018067, 2517004, 6643239, 7360694, 997615, 270850, 8140274, 6023690, 4560996, 5616972, 8378591, 2146042, 2118514, 4132833, 3897084, 7598211, 1365559, 1995659, 2691306, 8067806, 2950206, 1440985, 3680816, 5194745, 4792326, 8110768, 2753322, 5417772, 2112931, 6660315, 2243992, 5388111, 4349058, 7372825, 7815186, 2089480, 5479131, 7763636, 299565, 6089727, 7736424, 8314127, 3993237, 7723160, 54701, 1979067, 8072695, 5619833, 4545060, 5274772, 4556474, 3383305, 5411965, 596093, 2661680, 7720045, 4684761, 138457, 780297, 3009923, 5899548, 2186443, 5757308, 3802274, 6962253, 4372456, 1059200, 4391514, 6402874, 6241683, 6159932, 2541043, 4079381, 2973059, 5370494, 4816093, 1127357, 1713594, 1937266, 6124978, 6371858, 6821754, 4756042, 310259, 7968370, 4686235, 4973626, 175414, 7345333, 2749310, 5240062, 6190883, 3434125, 7036143, 7921069, 5785875, 8091122, 5877196, 4803033, 3014738, 7488849, 1320371, 7664956, 7468113, 3544523, 7133933, 7008153, 5966479, 4871324, 7848312, 6506451, 5466628, 3889260, 1298307, 4591979, 7591381, 7144223, 146034, 392421, 3567759, 2627997, 3415647, 4658965, 4833106, 3033871, 8093109, 4125445, 8222319, 2997711, 3806676, 6357234, 2669841, 6728316, 3960038, 1575245, 343553, 6527180, 6864842, 3741462, 8193684, 2261106, 6112912, 6893813, 3084354, 8004977, 4099815, 6626811, 7975210, 3705369, 6960780, 5347030, 5591966, 2729331, 7688439, 6118106, 6105173, 3846440, 6390518, 7815184, 2694289, 3328890, 8014375, 6407885, 1533483, 4198729, 1477821, 6292908, 7844058, 8360686, 1355243, 5378328, 8220114, 6394563, 6607678, 1100775, 2131609, 2821568, 1900840, 4281285, 4476333, 2441817, 2322614, 5415775, 5235530, 2585105, 2460481, 4195474, 5439495, 4603624, 735268, 7267546, 4697461, 855225, 2705354, 5244177, 4410228, 7107428, 6821377, 6688325, 1835360, 2200903, 3718892, 5745724, 7728283, 5931346, 331306, 6739251, 2705636, 6078543, 98487, 2212231, 5407185, 7909207, 4962529, 5398702, 6147711, 2696755, 6880922, 603941, 1717152, 5611631, 6490209, 3453456, 2060315, 5934591, 229634, 3423256, 6035737, 5705747, 2342288, 7568331, 5224191, 3689227, 6851817, 7408189, 2149440, 873240, 2840441, 8309526, 4084030, 288051, 4707883, 5562347, 1672810, 8344179, 1436140, 3443160, 1228202, 3223647, 6010183, 7965876],
[8325859, 3573398, 8139931, 5392248, 6351555, 1867569, 4833543, 1330958, 5198564, 4573208, 7764565, 2377632, 452799, 6030547, 353546, 3738360, 4424844, 7915247, 1979457, 7748700, 7686665, 2738123, 651356, 4412770, 5739709, 6846189, 1531347, 1850083, 3375967, 2428044, 7865030, 3986540, 8060902, 2919366, 2350659, 7548331, 2286547, 1385257, 6824713, 6530263, 4450265, 5714592, 4255919, 1894721, 1330715, 1541090, 7442571, 3169759, 6319712, 2590209, 7462426, 6643070, 6589458, 506299, 5554146, 8153739, 2598645, 736704, 611523, 4763309, 6402068, 2299999, 7669914, 3347316, 6342727, 3565299, 8348376, 630464, 6382340, 8135996, 4298851, 1542617, 6783308, 6881748, 3486990, 7543203, 1317244, 122321, 3161919, 7130136, 6453905, 2499456, 7305499, 2009503, 5764223, 2105350, 6778377, 6803545, 5825836, 827303, 2067915, 7049723, 3920884, 4538433, 8103139, 4453133, 5954137, 222248, 7211004, 7106486, 6352995, 1032237, 6434957, 287630, 882708, 4002065, 5466516, 7535284, 323430, 4854187, 4750337, 171878, 137625, 3218468, 3038107, 2887754, 4296786, 5621416, 4442940, 4667794, 2911821, 7976334, 4078180, 2183369, 1095462, 4055373, 5129823, 3026899, 7544294, 8200729, 3554044, 6434035, 6710692, 2895513, 7807743, 691188, 7653085, 2403520, 4720607, 2796471, 783728, 1786095, 4180633, 52734, 908169, 1945353, 6369898, 5037784, 3040747, 8188774, 2687163, 4105304, 5520706, 7473140, 485283, 5620690, 3255964, 5895476, 766607, 2742052, 3891144, 1784465, 3934637, 7475450, 378575, 6096711, 6686462, 3941896, 6965202, 468953, 4913668, 1115456, 7214830, 2877786, 8031118, 7997451, 5089082, 1301110, 3935697, 3494495, 4895605, 2571982, 6160703, 3962287, 6780869, 4609816, 1326908, 7129830, 2125955, 3488762, 7399442, 3225566, 8282331, 2867914, 7015269, 2066998, 2443475, 1739661, 1124159, 8191842, 7543653, 7603394, 4941714, 5199028, 7842606, 2881317, 152044, 8303753, 8118951, 8306620, 2437103, 3284790, 7147456, 2717504, 4769303, 567801, 804053, 6576600, 5525992, 3836856, 1970756, 2283912, 6177931, 4254691, 254880, 7180957, 95144, 1815261, 794858, 7426853, 5177510, 2516767, 4104888, 5572861, 4514389, 4064585, 1751133, 112220, 3316248, 3376968, 7797205, 6759748, 6702934, 2311338, 170374, 2133024, 3669160, 5478709, 6233837, 6290466, 6515132, 1763465, 3342498, 2191305, 942261, 6343200],
[772411, 4778555, 4565112, 3514677, 7105960, 1667058, 7430013, 7819448, 4210151, 3765940, 4002390, 289191, 6646917, 4937308, 1603724, 4448729, 922931, 4818660, 7963198, 4126482, 7141846, 1053176, 1650522, 6656308, 3473793, 3144025, 4924613, 7183816, 3029355, 3513109, 5398528, 5931253, 7508642, 688011, 6298052, 3809654, 4289748, 1943034, 3579609, 7344720, 92729, 1130566, 7147772, 1747431, 7654561, 3176266, 6251091, 4875249, 5979007, 801930, 7440141, 5752191, 2022116, 39201, 5788923, 813218, 7357372, 4378971, 8292135, 3237684, 1553914, 815461, 4689386, 3844914, 2611344, 2142374, 7695158, 6995757, 984755, 7868972, 3792247, 1886959, 5670710, 1711684, 2751208, 5940761, 2849841, 6265326, 3646861, 6929103, 121127, 8262205, 4700034, 7841278, 3948061, 3305258, 4354990, 1515798, 1827982, 7654188, 7520886, 7337376, 925253, 200124, 4613529, 3863051, 3099188, 1185611, 7833463, 7062363, 3551230, 1289569, 2737169, 375368, 1511419, 5184311, 3748442, 1648573, 2425722, 454579, 3674682, 573541, 4713120, 2983292, 3028325, 3614594, 4376551, 2200890, 66022, 7524339, 195082, 3529129, 7128783, 8337557, 5722533, 2129879, 6929577, 403522, 7897139, 2334014, 324475, 4666411, 3098130, 5310938, 4815466, 691438, 6694422, 2393305, 4011221, 1429701, 5612888, 81335, 3445461, 2039221, 6949625, 5813813, 1591964, 4036734, 5909304, 7189313, 4219628, 1748976, 6646310, 3113448, 5159383, 5814607, 8318667, 5912316, 6974854, 830971, 1632802, 667223, 7553318, 6236257, 5618861, 8176904, 4763905, 5637980, 6762582, 1816172, 5453479, 5457552, 88433, 1778303, 1569793, 2199800, 4804482, 6180449, 815444, 6123431, 7082238, 4852804, 4907731, 7773599, 3143969, 6925642, 1250047, 2607908, 1301528, 5589021, 2954362, 8211040, 7783308, 1833539, 6303774, 4283189, 7880936, 5695212, 2364702, 2912632, 2612112, 7420330, 5429041, 7224328, 4551856, 2533602, 5019279, 5535136, 7151916, 7184870, 3651531, 7956952, 131191, 6046812, 375845, 6780899, 5394795, 1487396, 6008990, 3904217, 3581462, 7611311, 1449825, 873480, 7515790, 5007586, 3510715, 4599889, 6470798, 7844070, 2304961, 4991710, 3358094, 2261629, 6675641, 3834364, 7596243, 3423712, 1441837, 2361981, 5524589, 847966, 8122106, 7693909, 2890737, 8117570, 482755, 8120680, 3343369, 7485319, 1130652, 8027255, 3957339, 4900464, 2053307, 1536181]]
NTT(c): [2690945, 121052, 7150318, 8287206, 2288451, 4023453, 386463, 4521262, 5904397, 5688061, 1610498, 2897472, 5173858, 8251051, 8034129, 7307004, 6477731, 2295177, 528991, 4283125, 470886, 3547028, 2050126, 7303776, 5180635, 769698, 7387421, 2869360, 5073979, 3058669, 6532114, 2177912, 6060654, 3407581, 1478148, 5785466, 117003, 773842, 8241771, 6381157, 1795475, 5643469, 4726601, 4005097, 2571179, 5789247, 1044612, 4900179, 7487018, 7703584, 4283361, 330233, 3726039, 431351, 3077645, 1613222, 2973554, 5349121, 2336354, 1505297, 3779321, 15000, 3830462, 6224987, 2818120, 2170426, 7175285, 7794091, 8005785, 5475062, 709647, 7834526, 6619698, 5130004, 6829708, 369152, 6387976, 3150488, 3277421, 4986217, 3130106, 1250471, 948833, 5817332, 2511825, 740837, 1596072, 775148, 5088015, 88353, 7540862, 813331, 3153995, 3975035, 2679818, 7173989, 3351079, 6264111, 6604952, 6952938, 3139300, 6973618, 3349753, 775931, 3575628, 5517357, 8116002, 4032702, 2506165, 7738504, 7317489, 509466, 84119, 6325618, 2082735, 5475407, 3827229, 8013830, 4599652, 3848224, 6744686, 1575503, 7160724, 1515678, 2119631, 2311035, 5615841, 134650, 1247324, 1340879, 4982117, 1471381, 6021607, 4191164, 2735447, 779278, 7132637, 8113556, 842804, 4248715, 511975, 6538824, 2975967, 1497099, 7209604, 4670012, 379903, 5795198, 3691658, 3108828, 1317681, 2245383, 7237183, 7668045, 522328, 7316344, 7458823, 4165622, 7067295, 5396050, 5275326, 205471, 5327072, 5003556, 3028175, 6840495, 3822188, 7103192, 7395788, 4827882, 6435889, 3219844, 7235969, 791555, 1080428, 880785, 3100269, 7379364, 1530478, 1139597, 6950901, 4803728, 4529523, 2135258, 3640627, 3760935, 7250092, 1969467, 1098969, 731816, 5978393, 792890, 3431781, 4972484, 4418752, 6878239, 261186, 1188342, 695676, 7978030, 7724988, 6231179, 7222462, 5897322, 2494301, 3919195, 6645882, 7884412, 2018759, 7087781, 7488498, 2347667, 798029, 7441875, 8087807, 4318891, 8366135, 1123836, 3515485, 7836306, 2153853, 7144330, 7935307, 3785902, 3939509, 1899969, 7418347, 3990633, 2129103, 6268676, 3761213, 3695313, 7668190, 3939129, 336075, 3155205, 521333, 2933008, 6947827, 5156973, 4925548, 848825, 6994707, 6023374, 7366844, 4854418, 236585, 6158594, 4342136, 4993509, 3905646, 2503545, 6571886, 3694025, 7822459, 7341964]
NTT(c) * (NTT(t1) * 2^d): [[6819480, 8012510, 6285477, 5689914, 2890547, 7501519, 6159655, 7652394, 1400460, 2698837, 2812858, 6495626, 7735135, 1993930, 7135851, 641420, 4392911, 8057521, 146059, 4077838, 5692793, 3258426, 1639608, 1429672, 5182577, 4643850, 3321782, 3253391, 7415252, 2261058, 3482782, 7582710, 1374024, 8110908, 5427979, 2682796, 3927775, 6969135, 7547126, 3020907, 5781921, 6447067, 230900, 158153, 1835843, 3858955, 97050, 3882824, 8155267, 4356433, 1825009, 7115136, 5644289, 5238443, 2098466, 4015153, 7982895, 3526376, 6593741, 2714299, 2958158, 1637991, 709629, 648309, 4813560, 7027296, 1676336, 1054056, 301823, 8357045, 127727, 5912268, 1155405, 3403527, 3310960, 1512430, 536209, 6273283, 5318522, 8096127, 4313971, 3575990, 1771746, 2911122, 5678491, 4907156, 1899087, 7679748, 2755281, 484044, 2752814, 4226241, 4172130, 6382224, 1696273, 732593, 5070876, 3255254, 3266392, 2064794, 1434708, 2363655, 405376, 5911748, 5780553, 4191420, 6071251, 2584719, 2238435, 317596, 2043922, 406177, 4068675, 8116952, 8252034, 1741079, 7627760, 4541838, 5151609, 3997926, 7372982, 4698794, 7300570, 7107562, 3250686, 4705508, 1518400, 3488236, 3384309, 522480, 2908861, 5706364, 6346578, 6318794, 4211006, 1429779, 4225560, 1028580, 6697824, 3702666, 2842372, 571095, 5311384, 3989826, 4293823, 3901429, 2654221, 4609542, 4576968, 2068070, 3295734, 5701685, 2827758, 4524988, 1521405, 5198979, 7117609, 5990035, 6979108, 1506042, 6905390, 3873428, 6845946, 7052297, 3822219, 2244647, 1786751, 3923819, 4777813, 4292560, 764688, 6320554, 1725679, 5346988, 7002453, 3253799, 1226036, 4705495, 258735, 3293166, 6144506, 1709802, 2621134, 1063641, 1021081, 6294947, 3640000, 4516075, 1246995, 7879961, 677751, 4785236, 3167132, 1825820, 3452480, 8200206, 6501092, 6526329, 4874401, 2290519, 6485724, 4103333, 788580, 2080647, 4613240, 2541498, 1236895, 6381617, 5574707, 2087198, 6174416, 2863589, 5043159, 8306776, 4888119, 1031262, 6733751, 1029393, 2490661, 3847948, 1784378, 1431298, 527688, 4908157, 3424141, 4950855, 1037816, 7351352, 4758323, 1764973, 4852236, 3133755, 2381938, 2911758, 3834952, 5103516, 1931627, 4361509, 5539983, 6422814, 4072832, 5607654, 4423923, 4764824, 3049642, 6452984, 2509187, 2382849, 5769543, 5024686, 3987713, 4958826, 3407047, 5787414, 2675317, 8091065],
[7747361, 294996, 7628437, 5308267, 8275015, 6227976, 5368317, 1110961, 1140611, 2833636, 8203334, 1139888, 7170282, 8374398, 546500, 3632862, 4504537, 7547277, 6834164, 7662123, 7588823, 1817707, 1219602, 3334382, 7920613, 2371613, 7517595, 658715, 3437116, 272900, 885839, 4685718, 1863880, 6160818, 7981695, 4393649, 5163526, 4497151, 7293135, 1024103, 957106, 790420, 1949196, 3706698, 4934884, 5078878, 470514, 3756260, 4819127, 1831083, 5224427, 1606949, 7186423, 8098609, 5923237, 3467791, 1728389, 4102474, 1516693, 2027818, 36188, 3951759, 2679484, 950310, 3935993, 7185861, 4107070, 3044579, 2083109, 7188675, 6826667, 1259883, 4086014, 5865742, 2371021, 4550061, 4288454, 1973404, 6353115, 5796481, 5394565, 5642734, 612460, 5279519, 5172757, 1984648, 7517074, 4154018, 6307035, 7875444, 5241526, 5629331, 8166769, 4602225, 5425864, 3564598, 4314169, 5809214, 1191939, 464287, 8154733, 6760133, 2744336, 5437418, 3450222, 2095525, 2916637, 4354780, 2223874, 7762181, 4545991, 5958532, 1794890, 8347297, 7616634, 7834298, 546317, 1992079, 111044, 7065316, 3797115, 1237450, 5441029, 6511799, 7725203, 2163622, 7884415, 4546877, 7223855, 1204971, 5918030, 4762643, 3326066, 8132903, 7491142, 4461626, 945950, 6730513, 1134615, 5189637, 1540313, 1572807, 6332738, 2071294, 1125085, 4510581, 1679510, 5962664, 7292242, 7213392, 6218166, 4220340, 3030010, 3846741, 5727237, 7065521, 7224550, 851159, 5685935, 3955557, 2429885, 7561362, 955274, 842340, 1494181, 4673837, 8275289, 735235, 112571, 2368173, 4226391, 3249636, 563797, 7789334, 8346138, 4743587, 309830, 1031259, 1504392, 4912333, 925256, 131929, 1271446, 4511488, 1710185, 2902790, 5272567, 7756566, 3703701, 8271716, 3532131, 5479238, 5171084, 506781, 1260891, 3547316, 4027930, 1814911, 2633684, 3410403, 2075159, 7990474, 1580040, 2185373, 2856944, 4608760, 5286421, 3469857, 3950152, 4532501, 5088855, 2313272, 1865285, 7349867, 7161692, 4122428, 6290832, 4975003, 4191082, 4754072, 8037184, 6058217, 7123466, 2259697, 7070498, 7375610, 6667315, 2104687, 4917388, 7269149, 6196104, 1782753, 682605, 3653302, 1980500, 199589, 1170580, 4263843, 5957847, 94066, 1159237, 5926770, 162179, 4784248, 5929100, 6021564, 1752028, 5355139, 1289963, 7167676, 8057108, 398130, 433659, 1874486, 4403869, 3530120],
[6003421, 134024, 3298140, 4670839, 1396842, 7513299, 444571, 6134764, 6379002, 7636717, 7584177, 5837769, 6358265, 913037, 1100196, 469322, 2523573, 1134766, 7996769, 409878, 4816845, 633871, 2312802, 1164388, 5835735, 4089323, 3395722, 4361907, 1393956, 5385468, 3853187, 7081125, 187870, 6994482, 6636052, 3290202, 5042753, 6072693, 2549384, 5674023, 6505135, 1738909, 1927498, 376226, 1708673, 7214524, 3284819, 7617368, 2801120, 987906, 3931692, 5361281, 8012359, 2364741, 6274710, 3943518, 2342559, 5647912, 1432919, 4184551, 5159630, 4996318, 365627, 2159887, 650490, 2221621, 210134, 2761881, 4656252, 7568240, 5883737, 725560, 6512439, 3457118, 5992118, 7305746, 7145841, 329330, 8075259, 4870247, 6666644, 6593629, 2347144, 3071975, 3865876, 7721206, 2814280, 4924000, 3123557, 597506, 5435582, 3981552, 5985533, 1161095, 6544116, 2471973, 8311302, 7896547, 2779949, 4823752, 7681159, 887234, 2155514, 2102000, 3528159, 7185815, 8109664, 1337832, 1444104, 7066666, 1993159, 2847205, 985319, 7785172, 7460396, 3193588, 3881625, 1451740, 7305835, 3395775, 1424066, 6727549, 3519858, 6355127, 8070942, 629206, 6115003, 508717, 4617081, 1644067, 6135682, 5750214, 6425687, 3335542, 6050764, 2180231, 6515009, 1809690, 300237, 6142619, 4774995, 7952270, 6964394, 2830262, 6719502, 2002834, 424376, 5011882, 2926767, 4113955, 4613967, 2664643, 5754779, 2653292, 3802204, 7990260, 246169, 1852274, 6756136, 7223000, 6369991, 5227640, 3142421, 5147019, 2058222, 5064169, 2905852, 8161393, 7125802, 6269219, 1086244, 7055455, 7085861, 6702991, 7714822, 5468892, 2207310, 7905958, 2131770, 5820928, 2034856, 232235, 6200416, 6099433, 2030877, 7761015, 6822268, 3057026, 5812857, 7820854, 2986593, 7860002, 3987855, 1914748, 5467437, 2705841, 2002587, 4996059, 3784996, 2839990, 6280456, 35657, 1018021, 6237061, 2865586, 7635992, 7993374, 2300456, 2366875, 7555154, 3162241, 2935966, 2072294, 5613967, 2110880, 5286770, 3900227, 7170162, 4584074, 1620830, 1094125, 311463, 2207618, 361196, 7299311, 6046790, 4860517, 4922094, 3303751, 1435251, 6815681, 5017774, 4348261, 8268075, 4417980, 347884, 739565, 8295855, 5145217, 7528454, 7675010, 635475, 1387222, 5819821, 1201580, 1332362, 6668597, 7363435, 1207190, 5898251, 2679448, 4609763, 3409812, 814623, 3974604, 2629323],
[3595031, 2172132, 2242460, 6930746, 3468245, 518574, 5535245, 7259602, 2508700, 5678394, 2678450, 1644180, 1805562, 2211183, 4785764, 7414977, 5169017, 4761493, 6937462, 2347750, 6233468, 4493077, 7682383, 696689, 477682, 1487051, 5198771, 6445587, 6535291, 1881896, 1276240, 2965152, 5118941, 6927280, 2904202, 8044305, 8282508, 458223, 5429459, 3159529, 6487529, 5916786, 1209575, 4483000, 8185341, 3469604, 56191, 6349451, 2068604, 1240373, 6815760, 977316, 4755271, 1423080, 2292900, 6261856, 919980, 1810884, 1426611, 214179, 5838941, 1618455, 7967706, 7085854, 1334040, 1048561, 1526830, 6118860, 7866407, 4328502, 606280, 7504132, 3128152, 1353757, 4034656, 488467, 8207498, 985068, 4872437, 7596495, 3127084, 7009075, 4692381, 2886056, 2771246, 3638220, 5175548, 7201746, 56429, 7323274, 2343565, 2063557, 4889841, 4684882, 6820030, 1664997, 5088824, 5888490, 2197478, 656361, 7287955, 1725934, 5022443, 476321, 2065870, 4703216, 2274255, 2480806, 2913865, 7823001, 3958703, 6056784, 7833705, 3522175, 1017322, 4608128, 7717466, 8188590, 941219, 8128679, 7764397, 6696469, 735356, 540697, 3504052, 4281991, 3503252, 5142298, 4519811, 6751218, 6674232, 6128522, 2967297, 2400455, 7387494, 2609170, 782443, 4347425, 1274634, 6816052, 2355179, 224125, 5721707, 2382610, 1105233, 8070353, 7872249, 4713412, 8106036, 4193355, 5259556, 5065518, 2108929, 3958473, 8282475, 2456450, 6739929, 1492496, 4822091, 661925, 5669115, 8267638, 3935070, 6258527, 6861391, 3088984, 4137003, 4323075, 4658917, 4881945, 5817063, 1463335, 2961250, 2925583, 7645347, 2592392, 1447844, 1246441, 5203674, 408196, 732458, 2911805, 540609, 4248752, 7698004, 2657785, 7803206, 6024758, 931799, 725849, 3828200, 1514629, 2994354, 2429836, 4980891, 4749878, 1239112, 6617360, 940695, 350101, 7245079, 1594392, 5493894, 2556786, 3410438, 5944993, 1096769, 3815736, 3466075, 4536904, 3767623, 2216862, 3453479, 968444, 1972993, 5220793, 126485, 4169087, 6203908, 2242501, 5790475, 4389903, 7048736, 7128421, 4493049, 6454525, 3823645, 5427403, 2514216, 7861379, 8229605, 5969721, 3848021, 6850804, 3490373, 6309703, 8206607, 6047760, 3829398, 6913163, 4727846, 5200601, 2954280, 4381167, 2535875, 5480783, 6797753, 168817, 1315333, 3565139, 7826672, 695583, 4895422, 3649272, 2556653, 4465034],
[3948113, 3370824, 1248431, 7061664, 875246, 1463966, 7339943, 1119644, 2208364, 5788360, 2318071, 351454, 5677860, 2036162, 774705, 7610264, 3893471, 879876, 6974988, 3698246, 7311222, 7980889, 1084825, 6617568, 398734, 716743, 5219038, 4149481, 4934276, 8215542, 6098705, 3401638, 1473797, 2113796, 446328, 7957736, 4806750, 5767673, 5344455, 7191414, 5820974, 7090641, 4870782, 6756101, 92727, 623115, 2322382, 4293223, 5018901, 2406218, 4808649, 2416386, 508610, 7293346, 2263764, 5939696, 5837395, 3731691, 7195314, 2147160, 7757197, 6188628, 2439198, 5179845, 7915608, 382501, 5053293, 2758606, 4736224, 6759543, 2178006, 5465498, 2856604, 8210707, 6445834, 2176015, 6141371, 5747320, 1002877, 3068489, 944997, 3962792, 4219457, 1867692, 7072747, 8248412, 2985241, 8164062, 3766524, 704885, 709980, 2652168, 3511368, 6909259, 3478318, 7685181, 7856446, 6128237, 3540295, 1163034, 6175224, 297980, 2917828, 2148403, 2790084, 6446018, 354769, 3587445, 6633293, 7387541, 2079100, 7400332, 3521498, 682614, 4970131, 2397383, 652315, 6513108, 4166117, 5393801, 3843297, 1159490, 1868274, 152971, 4695915, 3675777, 259453, 7130389, 1469547, 5503415, 6788111, 3929536, 2688926, 5315270, 6833281, 1440840, 1444362, 6225209, 2154197, 5039679, 3157257, 3340663, 1236000, 4490526, 2857146, 5664135, 5766557, 4873745, 5405783, 3861377, 5261916, 7175618, 847836, 4211170, 2806242, 2588769, 6843987, 6952175, 7172986, 3330242, 1050225, 4183848, 1242504, 3568286, 587527, 4442720, 3516073, 6622073, 7893560, 4671243, 8205923, 7375591, 835001, 2850375, 2898789, 1075940, 5391753, 4341310, 5911080, 523034, 6472848, 4013302, 451405, 4750194, 1387113, 4397951, 5945390, 6348754, 7326216, 4291074, 3645510, 126514, 6538473, 2564488, 7222972, 4239775, 7565549, 5825251, 6682878, 3833007, 8142442, 8141216, 379402, 8359743, 7594913, 7261072, 6083450, 3775391, 3724051, 6752598, 5710386, 404866, 6126101, 4470612, 3190095, 1386568, 6066761, 3249037, 6283841, 3645522, 3990700, 5522863, 7362800, 2878505, 2391065, 260572, 4106811, 7995413, 1523811, 76496, 469641, 7003985, 5350295, 980747, 7730746, 4877740, 2694394, 1280085, 1153312, 7251014, 639084, 6227876, 3563389, 1668992, 386400, 6647759, 7864906, 1634333, 7775022, 2824960, 3881492, 1362404, 1422504, 6868155, 3397457, 1637821],
[4494055, 3736852, 1736855, 703517, 3567399, 4102405, 935224, 3480087, 7768531, 5863235, 1452585, 6831407, 7038740, 2075344, 3097244, 5672863, 1446348, 7766252, 1566083, 5806586, 996792, 6839842, 332848, 833203, 2535658, 3780696, 3156458, 2940791, 475914, 8251602, 2861815, 4711596, 7821804, 6414390, 8080327, 1272509, 1830697, 3659322, 6586160, 2532277, 7237153, 1016342, 4036678, 1952018, 4781259, 3136557, 2408211, 7331023, 5399339, 1780149, 3058394, 7690781, 2131338, 6089462, 2970189, 5549965, 3438653, 3100726, 819376, 2603713, 3371721, 4886597, 4502285, 1670782, 1933904, 6619708, 4497174, 881868, 1982014, 5930122, 3678101, 5020086, 2538314, 3497055, 4821139, 6001610, 3106052, 2437304, 5632992, 7344532, 1903965, 1497611, 638359, 3744268, 5951047, 138550, 511557, 8183453, 3538705, 4342132, 2601669, 3652922, 6147578, 5581449, 6748464, 7849378, 7687428, 6318085, 102901, 6985196, 8168904, 3151278, 1818314, 6655190, 965759, 7259141, 7627160, 2067312, 4519326, 5950313, 5605630, 8019984, 2173844, 106767, 4450088, 4513801, 6123441, 6984245, 5433932, 3919313, 7843584, 6440314, 7326391, 3033504, 2007446, 3750649, 6063470, 3993889, 7527155, 5531741, 6735109, 1215908, 7967874, 4448974, 3637281, 3510749, 6381173, 194382, 4505467, 6049688, 4964083, 5606803, 3949615, 5230532, 3178515, 3174168, 2345853, 6921176, 7230413, 67840, 1897346, 7289106, 1875684, 2843313, 7889351, 3372202, 5398070, 3555948, 6179274, 2187866, 2642512, 8115747, 5074456, 841266, 8067320, 71854, 6248224, 4866754, 834021, 1408944, 2972216, 5436272, 3326125, 7889760, 2758110, 6813017, 1038198, 3163291, 7402592, 4448079, 8110884, 4277339, 4198955, 44160, 2987878, 251748, 4072176, 7154493, 2872740, 5431950, 4882742, 7233312, 7102460, 3317402, 706282, 3148610, 506973, 2457644, 7332286, 4445283, 6574133, 4048715, 1402229, 493773, 2205643, 740851, 6806440, 2999188, 2874219, 7914590, 3200304, 5682138, 6053375, 6223045, 206841, 1446902, 1091708, 6054985, 5458667, 7728409, 3476262, 7423742, 2405335, 5511177, 6261090, 4266402, 5883460, 3442937, 526627, 4212160, 75780, 4506955, 3894377, 4187206, 2994422, 8212161, 6098569, 7058782, 2012245, 4307357, 3660339, 5865071, 8145323, 4439816, 5179073, 7943123, 4268799, 5745514, 48752, 7107651, 8190131, 2175461, 6423995, 6711321, 2599713, 2510042]]
wPrimeApprox: [[4758519, 960760, 4935710, 3304526, 5646329, 3801955, 7832341, 837485, 3649919, 4113435, 3451213, 365211, 7283435, 4186002, 642582, 595189, 7466745, 3706267, 7975728, 7353938, 2276138, 5658000, 8233178, 2183980, 4608632, 5474365, 2425574, 6559285, 2804609, 5597201, 2641918, 5544548, 1014922, 1578291, 3510017, 8336297, 1770798, 6225246, 3175092, 363064, 5775612, 8357939, 7012368, 1857795, 4816431, 2981862, 6365635, 345219, 861927, 3327281, 6291776, 7273761, 125994, 2939614, 515722, 1185805, 8103298, 4642804, 1191088, 7255921, 3401689, 4681503, 2685603, 8064073, 4874160, 1040989, 5526614, 1774182, 3827569, 2475072, 1808512, 5873015, 5537521, 5308641, 3446953, 3251726, 577868, 3998185, 8001698, 1193419, 3653031, 306323, 3670718, 2687952, 4437003, 3514480, 294569, 4598149, 1540863, 904047, 4382683, 5315922, 4359326, 7510500, 2976706, 207667, 820857, 1419026, 4693582, 1067202, 6825895, 2913886, 2198084, 6312548, 4847365, 4885859, 5385714, 7127874, 1706984, 4170363, 5404789, 2580613, 6077839, 695831, 4627762, 6339919, 634344, 2564633, 1572647, 6253418, 6289916, 4440931, 6240918, 1500492, 1427383, 7483141, 941869, 1048032, 7519468, 5821506, 2914323, 5818567, 399727, 6020921, 7171577, 5042607, 4988125, 6897478, 1043154, 4093185, 6875213, 7985618, 7812975, 523656, 4673218, 6904002, 1478383, 7540191, 6008615, 6877268, 4976149, 4639864, 5437728, 2316032, 7920620, 3135552, 1859893, 2962102, 4942708, 2604530, 6267321, 1608507, 5873358, 4484699, 861117, 2549994, 3381865, 1967159, 7158810, 4583027, 5345549, 6940002, 63549, 2154488, 2470260, 6776477, 7522593, 8356707, 1673423, 5906136, 6653428, 5031579, 7811789, 4336365, 5782332, 665530, 4911530, 1190227, 1171577, 8295892, 8181078, 5220968, 5641229, 1541547, 4536269, 6770939, 5465591, 2954758, 2469404, 2153593, 6164668, 5415927, 293027, 7504671, 1184865, 5613926, 3056131, 2035570, 6610621, 3963412, 7716911, 431402, 579731, 4547383, 501607, 1013302, 2661948, 1291077, 1087192, 5989300, 1325579, 7460582, 3655582, 1991023, 7458991, 7892419, 3281032, 6199113, 397945, 7238619, 1901786, 5106678, 7010865, 5619314, 7930764, 2074435, 5099130, 7326247, 4602993, 2668726, 6155015, 4849298, 3590550, 1361121, 3948653, 5236722, 3584499, 7789496, 1741671, 4857887, 726649, 8266945, 94022, 5081514, 607476, 2940254],
[4575140, 3628620, 6991943, 2364461, 7491971, 7649378, 7959176, 1450077, 4923388, 5154437, 7829539, 5750299, 2310686, 2331453, 2939618, 6441119, 976930, 7833676, 6325703, 1699575, 7766339, 4775427, 4339967, 3672552, 3269056, 581036, 4950590, 644466, 645566, 2656323, 1381262, 8032694, 1437953, 1274493, 4434493, 2171996, 6811451, 154955, 6020193, 3302501, 8142298, 615458, 4698720, 6964032, 188769, 6346477, 2745558, 2131857, 6872845, 2142070, 3276001, 5976172, 6154364, 325907, 1172807, 974710, 7286124, 3210797, 3421332, 6758637, 2493168, 5768980, 7000039, 3717756, 3110317, 2393031, 3152865, 6480557, 2770809, 5221236, 8334899, 6135994, 2638588, 3730399, 3780066, 1346048, 6978182, 468888, 6909885, 6712967, 688959, 1621861, 989666, 3335439, 1419116, 3325788, 6950816, 2580969, 7954552, 6055510, 5768186, 56088, 5610046, 3762737, 6282085, 5158209, 3423314, 4478078, 4170019, 5111643, 6479548, 2801004, 2998930, 5231146, 7362542, 5834718, 1985022, 6510420, 3693928, 5248807, 3060673, 339139, 3552956, 7133988, 889992, 4296378, 5225499, 2396168, 4334119, 3710497, 8373796, 3457465, 3174302, 2779972, 2508176, 6367593, 5551025, 2735778, 446010, 7617069, 1092561, 2043448, 5717631, 3918093, 1109893, 4242492, 7284596, 2923966, 2945424, 5845761, 132532, 4419447, 2375873, 2986980, 4695923, 7861533, 4320792, 5017218, 1378500, 6321453, 4174471, 5196148, 5907311, 5837953, 275047, 5614837, 2724517, 8197766, 2117779, 5833020, 2654519, 901838, 7965826, 3314227, 4431082, 3530244, 5986887, 8006689, 3766829, 1414188, 6485099, 1264890, 6664133, 3719186, 8100718, 1177022, 3926748, 5097633, 5986277, 3279856, 252700, 2582825, 2685313, 7440094, 6199053, 4256995, 2164369, 2765054, 5335974, 2057638, 5731022, 4769963, 2230308, 2869238, 2032353, 5874109, 1267053, 3663833, 4142814, 6548603, 6671404, 2253628, 1394559, 5382044, 3738664, 1910681, 4456506, 3814281, 4404803, 1176542, 3160494, 6254241, 4324302, 6214651, 2845493, 7674127, 7097689, 5875942, 1516393, 3361161, 8030700, 2642557, 4441611, 4434832, 1132361, 4971966, 6712095, 5071841, 92740, 2494787, 6813986, 1341916, 7826440, 2701870, 7296026, 2640458, 6866308, 1045578, 2940585, 6424459, 1608703, 4544318, 1319058, 591221, 3677992, 5418122, 357418, 1680200, 34536, 4332638, 4103914, 8246604, 1678954, 6082241, 6267539, 2321786],
[4548405, 5564275, 2079952, 1909722, 7280465, 7340170, 2314051, 2714236, 1984491, 6644267, 2288612, 5829011, 3844828, 5706010, 682088, 5701977, 6286406, 1988161, 2683955, 2440550, 5351718, 4745349, 2469601, 915940, 2590497, 6672625, 4593521, 5879633, 3831704, 4976839, 517099, 6628684, 3420840, 5894536, 793683, 3132360, 4996134, 585495, 246768, 2733469, 4175012, 465828, 248283, 5571594, 3153122, 1929677, 3556034, 4458578, 1421962, 4634619, 4835145, 6670113, 923385, 2251231, 6664664, 5478553, 3773103, 2208639, 2937788, 3177849, 6760501, 7457609, 6047263, 6364257, 440795, 7849198, 6942487, 292611, 6702626, 5238094, 1770177, 4263623, 3289565, 2854983, 3672481, 4302929, 756165, 8109786, 828601, 4961755, 7203092, 3463418, 5592321, 6241279, 5329421, 4631509, 7087090, 4675813, 2782001, 2293158, 7728285, 2677295, 162854, 4565924, 2385436, 7951733, 3847240, 2969685, 3306249, 3367877, 6914026, 7979751, 7730740, 798034, 6448415, 2569394, 2835250, 3376042, 6306021, 5746067, 2662061, 8277779, 6941554, 3416146, 5504092, 2721403, 7589771, 3329588, 5800190, 221448, 3367598, 716473, 3547654, 544366, 3266793, 3546665, 6091639, 1091948, 6830061, 2195976, 5928001, 7738239, 5268762, 1894003, 85106, 50767, 7983151, 19774, 5837497, 4551157, 5188730, 6840380, 3764680, 143572, 214983, 5657387, 4943420, 4787718, 2646515, 6882304, 1810767, 4880128, 3328311, 3031091, 2017318, 1228014, 5568480, 7887074, 5817102, 7944919, 3435329, 6742604, 3701232, 2370525, 2874795, 7045926, 7915303, 4177124, 2040448, 6823274, 7300343, 6246984, 326915, 1660874, 4573514, 3766576, 5461083, 6678563, 1062657, 3351990, 6232995, 2493311, 1823116, 6843536, 2524849, 3958210, 8064106, 5823985, 80225, 4087350, 1324262, 4500953, 2021524, 4527884, 307539, 577796, 1413302, 6237390, 4904401, 7674515, 1017140, 5218079, 358364, 5845446, 2957813, 2537260, 1923236, 6435967, 2994933, 7042132, 1911604, 1241748, 4216622, 926004, 7809410, 4363198, 1636668, 8193903, 3057821, 4311624, 4331550, 4127970, 7149448, 6214337, 7216301, 5629714, 7124219, 3597959, 7868871, 5064550, 5525976, 7248357, 56131, 1326101, 7507053, 591493, 6263002, 8089313, 6480900, 7698643, 1686827, 3881673, 5646022, 6637277, 2138980, 6888268, 3473801, 5127837, 2840172, 1058295, 1587850, 1163863, 3404555, 6843575, 3285438, 3631634],
[6871063, 8017117, 6397070, 4291496, 7466141, 1610329, 7200177, 7817341, 4014633, 7836615, 6607332, 644578, 7182533, 6896730, 6024781, 2218410, 8072750, 4958074, 1650185, 2301367, 2996096, 2962850, 3370355, 2776701, 6288756, 3841608, 8208305, 3526834, 7628209, 5527351, 7424063, 443024, 8347843, 2590508, 2664694, 2721036, 4982334, 1061568, 2236078, 6798443, 2117123, 3659513, 8050265, 7659195, 4192474, 627917, 7652308, 5027929, 4905425, 1059791, 5512850, 6491468, 7996584, 6913464, 1110277, 8272241, 2375853, 2900462, 278852, 1241652, 6354537, 4109934, 71271, 3686656, 2792870, 697762, 4105656, 1537319, 7509321, 3675418, 2049995, 3134492, 3433985, 7838424, 6004746, 5928560, 7179645, 2057730, 2339822, 8000943, 3806963, 2832508, 697191, 1057733, 1998333, 8222800, 1690808, 77452, 3246345, 3378035, 4316422, 2278748, 3541094, 1798932, 5751579, 7347445, 8186431, 6949022, 2180526, 323692, 6650386, 5919442, 374395, 7103097, 4821502, 6181196, 1163059, 3667160, 3079140, 2958979, 7977509, 5151244, 5103552, 7436689, 4497555, 3495681, 3857440, 1050012, 6043673, 6892241, 6412403, 2189577, 3510557, 2013400, 4298095, 2164814, 446299, 1557800, 7037144, 6003928, 8360683, 3050157, 4311852, 349423, 1962420, 2628809, 3142370, 4974505, 6705303, 2019688, 4803009, 2205196, 1186457, 4126247, 7735462, 4868648, 2370388, 8142950, 8235998, 3117085, 4642303, 6562549, 2167037, 614491, 1844066, 1430185, 3778739, 5307641, 3567876, 7122860, 4241183, 3167461, 4237069, 3320888, 2849070, 5528613, 225099, 4619911, 5016914, 3446506, 8124166, 7083113, 7275991, 1471163, 4815496, 3019710, 8246118, 6209151, 6396903, 1404838, 236016, 1290559, 6744425, 6082287, 5937807, 7637590, 2556007, 7493690, 5902339, 3534722, 5910366, 4084848, 2456266, 2372159, 5412490, 3451482, 2255954, 7707092, 2931015, 1394087, 5895301, 103837, 2861253, 7725436, 1706204, 5172440, 6892077, 5668352, 2652730, 3453482, 1575161, 466915, 7759592, 2147913, 1778708, 1787727, 7273918, 8079309, 563991, 6697606, 5385187, 4509798, 1355181, 5920781, 3169715, 4977809, 1178150, 7946938, 7752477, 7556116, 1569747, 4006177, 2512976, 2845782, 4009733, 5144659, 1410342, 7445250, 4636962, 6277633, 6549700, 3943432, 1994544, 4528971, 1664313, 3286177, 2842497, 4320750, 3389961, 6606944, 6172154, 4334749, 4533715, 5469776, 5083346, 7596029],
[5595749, 6889593, 1954500, 5039824, 3952028, 4107402, 3616353, 2872817, 5679256, 2187198, 5362646, 729712, 6646792, 2885262, 327434, 5146146, 2055155, 2922099, 2415462, 2253774, 310773, 3242220, 5760359, 1495077, 1907676, 8032998, 3256938, 7034984, 2819134, 5739344, 5457888, 7128617, 1533074, 5439388, 4550077, 5054309, 4317530, 2427727, 4327122, 6698375, 590002, 7370133, 800983, 5469617, 2705699, 3499459, 3470134, 1238656, 686528, 4727740, 1480521, 2493681, 2420683, 6426462, 6026502, 5309234, 5773111, 3527761, 5133064, 1803160, 2443838, 7688202, 4071495, 348119, 7230509, 7375103, 5847529, 2346907, 1423898, 2819880, 4794680, 7122970, 241845, 5237190, 2911427, 7100340, 6868090, 4286108, 5328458, 6858852, 527949, 8181432, 869391, 4179049, 4762437, 2696808, 7608662, 7847802, 7465995, 5606983, 1191813, 6583894, 959335, 5605194, 2802994, 3437820, 5210073, 8333482, 7265661, 2001854, 2672171, 2187756, 6134559, 5973878, 4271720, 4434483, 8297673, 5490451, 7181818, 5224902, 1946257, 6418621, 3019975, 4286695, 3382228, 6054776, 6508409, 7594881, 7469243, 3328290, 4231894, 288092, 1219249, 921919, 2247668, 714850, 693379, 1736487, 2888614, 2638598, 1203099, 1337671, 4857879, 1498076, 4862390, 6700417, 7015071, 7900226, 8128933, 5729602, 7791169, 2895633, 6701556, 1420248, 4467089, 3957447, 5055396, 6782655, 4631215, 2523314, 4441651, 227245, 7586887, 1524343, 3818312, 2153795, 4115858, 2655560, 1609285, 5124048, 5458508, 1060497, 5635191, 4998887, 5300886, 6707322, 3394923, 2906108, 5522677, 4948203, 7208401, 3111515, 2635734, 3046167, 4687513, 3938154, 7783176, 7535898, 3295728, 3524483, 4953164, 2506024, 5589487, 4529991, 4255640, 3099909, 6823488, 2878159, 2999026, 8037695, 3546625, 3616618, 5811028, 2071120, 3132746, 8056666, 5862287, 6795586, 5192206, 6116176, 2543113, 6119873, 3814202, 6296188, 5025406, 4086351, 4194741, 3644479, 1414235, 3240889, 3934948, 7070573, 2331064, 4827710, 7329446, 4638840, 4351624, 89560, 3551935, 1360140, 3821502, 5695459, 2363868, 56759, 6639094, 5539764, 2906067, 6250770, 7863087, 261721, 6766409, 6155631, 2020537, 5965648, 2638334, 597138, 7847056, 5743761, 1704402, 1740406, 1746353, 1660851, 6301629, 6099802, 2589232, 5031781, 4047070, 969482, 6654606, 3358191, 4799160, 6695746, 4135535, 7977457, 2451601, 7477406],
[5592471, 4577459, 5553834, 2487682, 2314501, 4003068, 8204143, 420861, 4049730, 773376, 7737452, 3744586, 6108957, 6800947, 34541, 2791688, 5275372, 4711732, 4101739, 4540077, 7985514, 2854015, 131009, 7987112, 3269031, 5210578, 6674670, 5937407, 6826525, 6869927, 828092, 3254539, 8360277, 983379, 67137, 7484747, 24602, 2625350, 8376909, 5603595, 6070602, 3578388, 8078665, 6668833, 2216855, 779249, 93681, 2882639, 2851381, 8035713, 8008242, 7699273, 1636399, 6010282, 803065, 4710233, 5615995, 1670338, 2958802, 4334172, 6369826, 6990186, 6118205, 1973157, 7310570, 3697010, 6991036, 5915009, 1273355, 7261235, 631715, 5641499, 7780677, 4846475, 7764632, 1966790, 5374581, 1759064, 4219636, 487538, 5019276, 8268702, 4284171, 3528279, 4248113, 274554, 8131791, 992479, 3720489, 7374753, 5156747, 3900712, 1301413, 4484049, 7591657, 3518277, 6508608, 4395082, 5307095, 5265026, 5011818, 7166097, 247687, 6464908, 706809, 3729653, 6702663, 1498758, 5718860, 7076924, 5357536, 7251849, 1301496, 1235625, 8196838, 4835876, 2657271, 4627595, 2065508, 1586472, 824787, 7253236, 7004603, 6393627, 7921756, 404141, 597838, 4837897, 1848399, 5994751, 1165818, 6130451, 2739319, 3690755, 1394985, 3583281, 8198761, 3442245, 4380828, 2442569, 7218461, 8019747, 3134434, 3220564, 5453283, 8375015, 1293851, 7229420, 2943425, 8229254, 544243, 8122979, 8075664, 546447, 1894926, 1722068, 1641632, 353997, 164819, 5250033, 6896600, 6391498, 3062108, 1493390, 1240031, 3004493, 3113425, 6198033, 3074022, 5279526, 6983053, 5753547, 4428246, 4857968, 7189447, 1663391, 7804732, 6716177, 742994, 4658459, 8178270, 2567062, 6890982, 5896432, 4182217, 2073209, 2399275, 323935, 8373194, 5251819, 55529, 4680175, 688911, 168988, 7004624, 2667940, 4612355, 6807498, 7725712, 6903394, 77210, 7900720, 6796518, 7875182, 3640661, 914135, 3376847, 636225, 7461816, 1770055, 5433771, 3515052, 4582278, 3171556, 1003805, 5570692, 3049189, 268819, 7446459, 619248, 6358697, 640267, 190378, 3955620, 6050848, 6085402, 6615842, 6047539, 4888294, 7949350, 3801226, 3205817, 3903714, 7009880, 822889, 5040977, 265282, 3580521, 346678, 6200910, 7066637, 5669763, 1784368, 3604964, 5570528, 626724, 7528016, 7869621, 6763999, 5204377, 6649831, 6767439, 7263780, 2720937, 8347901, 3210724]]
w1Prime: [[9, 2, 9, 6, 11, 7, 15, 2, 7, 8, 7, 1, 14, 8, 1, 1, 14, 7, 15, 14, 4, 11, 0, 4, 9, 10, 5, 13, 5, 11, 5, 11, 2, 3, 7, 0, 3, 12, 6, 1, 11, 0, 13, 4, 9, 6, 12, 1, 2, 6, 12, 14, 0, 6, 1, 2, 15, 9, 2, 14, 7, 9, 5, 15, 9, 2, 11, 3, 7, 5, 3, 11, 11, 10, 7, 6, 1, 8, 15, 2, 7, 1, 7, 5, 9, 7, 1, 9, 3, 2, 8, 10, 8, 14, 6, 0, 2, 3, 9, 2, 13, 6, 4, 12, 9, 9, 10, 14, 3, 8, 10, 5, 12, 1, 9, 12, 1, 5, 3, 12, 12, 8, 12, 3, 3, 14, 2, 2, 14, 11, 6, 11, 1, 11, 14, 10, 10, 13, 2, 8, 13, 15, 15, 1, 9, 13, 3, 14, 11, 13, 9, 9, 10, 4, 15, 6, 4, 6, 9, 5, 12, 3, 11, 9, 2, 5, 6, 4, 14, 9, 10, 13, 0, 4, 5, 13, 14, 0, 3, 11, 13, 10, 15, 8, 11, 1, 9, 2, 2, 0, 0, 10, 11, 3, 9, 13, 10, 6, 5, 4, 12, 10, 1, 14, 2, 11, 6, 4, 13, 8, 15, 1, 1, 9, 1, 2, 5, 3, 2, 11, 3, 14, 7, 4, 14, 15, 6, 12, 1, 14, 4, 10, 13, 11, 15, 4, 10, 14, 9, 5, 12, 9, 7, 3, 8, 10, 7, 15, 3, 9, 1, 0, 0, 10, 1, 6],
[9, 7, 13, 5, 14, 15, 15, 3, 9, 10, 15, 11, 4, 4, 6, 12, 2, 15, 12, 3, 15, 9, 8, 7, 6, 1, 9, 1, 1, 5, 3, 15, 3, 2, 8, 4, 13, 0, 11, 6, 0, 1, 9, 13, 0, 12, 5, 4, 13, 4, 6, 11, 12, 1, 2, 2, 14, 6, 7, 13, 5, 11, 13, 7, 6, 5, 6, 12, 5, 10, 0, 12, 5, 7, 7, 3, 13, 1, 13, 13, 1, 3, 2, 6, 3, 6, 13, 5, 15, 12, 11, 0, 11, 7, 12, 10, 7, 9, 8, 10, 12, 5, 6, 10, 14, 11, 4, 12, 7, 10, 6, 1, 7, 14, 2, 8, 10, 5, 8, 7, 0, 7, 6, 5, 5, 12, 11, 5, 1, 15, 2, 4, 11, 8, 2, 8, 14, 6, 6, 11, 0, 8, 5, 6, 9, 15, 8, 10, 3, 12, 8, 10, 11, 11, 1, 11, 5, 0, 4, 11, 5, 2, 15, 6, 8, 7, 11, 15, 7, 3, 12, 2, 13, 7, 0, 2, 8, 10, 11, 6, 0, 5, 5, 14, 12, 8, 4, 5, 10, 4, 11, 9, 4, 5, 4, 11, 2, 7, 8, 13, 13, 4, 3, 10, 7, 4, 8, 7, 8, 2, 6, 12, 8, 12, 5, 15, 14, 11, 3, 6, 15, 5, 8, 8, 2, 9, 13, 10, 0, 5, 13, 3, 15, 5, 14, 5, 13, 2, 6, 12, 3, 9, 3, 1, 7, 10, 1, 3, 0, 8, 8, 0, 3, 12, 12, 4],
[9, 11, 4, 4, 14, 14, 4, 5, 4, 13, 4, 11, 7, 11, 1, 11, 12, 4, 5, 5, 10, 9, 5, 2, 5, 13, 9, 11, 7, 10, 1, 13, 7, 11, 2, 6, 10, 1, 0, 5, 8, 1, 0, 11, 6, 4, 7, 9, 3, 9, 9, 13, 2, 4, 13, 11, 7, 4, 6, 6, 13, 14, 12, 12, 1, 15, 13, 1, 13, 10, 3, 8, 6, 5, 7, 8, 1, 15, 2, 10, 14, 7, 11, 12, 10, 9, 14, 9, 5, 4, 15, 5, 0, 9, 5, 15, 7, 6, 6, 6, 13, 15, 15, 1, 12, 5, 5, 6, 12, 11, 5, 0, 13, 7, 10, 5, 14, 6, 11, 0, 6, 1, 7, 1, 6, 7, 12, 2, 13, 4, 11, 15, 10, 4, 0, 0, 15, 0, 11, 9, 10, 13, 7, 0, 0, 11, 9, 9, 5, 13, 3, 9, 6, 6, 4, 2, 11, 15, 11, 15, 7, 13, 7, 5, 6, 13, 15, 8, 4, 13, 14, 12, 1, 3, 9, 7, 10, 13, 2, 6, 12, 5, 3, 13, 5, 8, 15, 11, 0, 8, 3, 9, 4, 9, 1, 1, 3, 12, 9, 15, 2, 10, 1, 11, 6, 5, 4, 12, 6, 13, 4, 2, 8, 2, 15, 8, 3, 0, 6, 8, 8, 8, 14, 12, 14, 11, 14, 7, 15, 10, 10, 14, 0, 3, 14, 1, 12, 15, 12, 15, 3, 7, 11, 13, 4, 13, 7, 10, 5, 2, 3, 2, 7, 13, 6, 7],
[13, 15, 12, 8, 14, 3, 14, 15, 8, 15, 13, 1, 14, 13, 12, 4, 15, 9, 3, 4, 6, 6, 6, 5, 12, 7, 0, 7, 15, 11, 14, 1, 0, 5, 5, 5, 10, 2, 4, 13, 4, 7, 15, 15, 8, 1, 15, 10, 9, 2, 11, 12, 15, 13, 2, 0, 5, 5, 0, 2, 12, 8, 0, 7, 5, 1, 8, 3, 14, 7, 4, 6, 7, 15, 11, 11, 14, 4, 5, 15, 7, 5, 1, 2, 4, 0, 3, 0, 6, 6, 8, 4, 7, 3, 11, 14, 0, 13, 4, 1, 13, 11, 1, 14, 9, 12, 2, 7, 6, 6, 15, 10, 10, 14, 9, 7, 7, 2, 12, 13, 12, 4, 7, 4, 8, 4, 1, 3, 13, 11, 0, 6, 8, 1, 4, 5, 6, 9, 13, 4, 9, 4, 2, 8, 15, 9, 5, 0, 0, 6, 9, 13, 4, 1, 4, 3, 7, 10, 7, 14, 8, 6, 8, 6, 5, 11, 0, 9, 10, 7, 0, 14, 14, 3, 9, 6, 0, 12, 12, 3, 0, 2, 13, 12, 11, 15, 5, 14, 11, 7, 11, 8, 5, 5, 10, 7, 4, 15, 6, 3, 11, 0, 5, 15, 3, 10, 13, 11, 5, 7, 3, 1, 15, 4, 3, 3, 14, 15, 1, 13, 10, 9, 3, 11, 6, 10, 2, 15, 15, 14, 3, 8, 5, 5, 8, 10, 3, 14, 9, 12, 12, 8, 4, 9, 3, 6, 5, 8, 6, 13, 12, 8, 9, 10, 10, 15],
[11, 13, 4, 10, 8, 8, 7, 6, 11, 4, 10, 1, 13, 6, 1, 10, 4, 6, 5, 4, 1, 6, 11, 3, 4, 15, 6, 13, 5, 11, 10, 14, 3, 10, 9, 10, 8, 5, 8, 13, 1, 14, 2, 10, 5, 7, 7, 2, 1, 9, 3, 5, 5, 12, 12, 10, 11, 7, 10, 3, 5, 15, 8, 1, 14, 14, 11, 5, 3, 5, 9, 14, 0, 10, 6, 14, 13, 8, 10, 13, 1, 0, 2, 8, 9, 5, 15, 15, 14, 11, 2, 13, 2, 11, 5, 7, 10, 0, 14, 4, 5, 4, 12, 11, 8, 8, 0, 10, 14, 10, 4, 12, 6, 8, 6, 12, 12, 15, 14, 6, 8, 1, 2, 2, 4, 1, 1, 3, 5, 5, 2, 3, 9, 3, 9, 13, 13, 15, 0, 11, 15, 6, 13, 3, 8, 8, 10, 13, 9, 5, 8, 0, 14, 3, 7, 4, 8, 5, 3, 10, 10, 2, 11, 10, 10, 13, 6, 6, 10, 10, 14, 6, 5, 6, 9, 8, 15, 14, 6, 7, 9, 5, 11, 9, 8, 6, 13, 5, 6, 15, 7, 7, 11, 4, 6, 15, 11, 13, 10, 12, 5, 12, 7, 12, 10, 8, 8, 7, 3, 6, 8, 13, 4, 9, 14, 9, 8, 0, 7, 3, 7, 11, 5, 0, 13, 11, 6, 12, 15, 1, 13, 12, 4, 11, 5, 1, 15, 11, 3, 3, 3, 3, 12, 12, 5, 10, 8, 2, 13, 6, 9, 13, 8, 15, 5, 14],
[11, 9, 11, 5, 4, 8, 0, 1, 8, 1, 15, 7, 12, 13, 0, 5, 10, 9, 8, 9, 15, 5, 0, 15, 6, 10, 13, 11, 13, 13, 2, 6, 0, 2, 0, 14, 0, 5, 0, 11, 12, 7, 15, 13, 4, 2, 0, 5, 5, 15, 15, 15, 3, 11, 2, 9, 11, 3, 6, 8, 12, 13, 12, 4, 14, 7, 13, 11, 2, 14, 1, 11, 15, 9, 15, 4, 10, 3, 8, 1, 10, 0, 8, 7, 8, 0, 0, 2, 7, 14, 10, 7, 2, 9, 14, 7, 12, 8, 10, 10, 10, 14, 1, 12, 1, 7, 13, 3, 11, 13, 10, 14, 3, 2, 0, 9, 5, 9, 4, 3, 2, 14, 13, 12, 15, 1, 1, 9, 4, 11, 2, 12, 5, 7, 3, 7, 0, 7, 8, 5, 14, 15, 6, 6, 10, 0, 2, 14, 6, 0, 1, 0, 15, 1, 4, 3, 3, 1, 0, 10, 13, 12, 6, 3, 2, 6, 6, 12, 6, 10, 13, 11, 8, 9, 14, 3, 15, 13, 1, 9, 0, 5, 13, 11, 8, 4, 5, 1, 0, 10, 0, 9, 1, 0, 13, 5, 9, 13, 15, 13, 0, 15, 13, 15, 7, 2, 6, 1, 14, 3, 10, 7, 9, 6, 2, 11, 6, 1, 14, 1, 12, 1, 0, 8, 12, 12, 13, 12, 9, 15, 7, 6, 7, 13, 2, 10, 1, 7, 1, 12, 14, 11, 3, 7, 11, 1, 14, 15, 13, 10, 13, 13, 14, 5, 0, 6]]
w1EncodeTemp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
cTilde: F7789A45A3587330E7FCF70695F7F69688A2B8D0CE54F090214F109F56484F98C3AD1A53A5441C2CA72A3B3191BC046F
cTildePrime: F7789A45A3587330E7FCF70695F7F69688A2B8D0CE54F090214F109F56484F98C3AD1A53A5441C2CA72A3B3191BC046F
cTilde == cTildePrime, signature verified
