precomp.py

psis_bitrev_montgomery = [4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041, 8775, 2344, 11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118, 2683, 1190, 4789, 7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973, 382, 3988, 468, 6843, 5339, 6196, 3710, 11316, 1254, 5435, 10930, 3998, 10256, 10367, 3879, 11889, 1728, 6137, 4948, 5862, 6136, 3643, 6874, 8724, 654, 10302, 1702, 7083, 6760, 56, 3199, 9987, 605, 11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689, 4080, 11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142, 241, 12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968, 12097, 7591, 5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821, 11502, 8807, 12138, 2127, 2839, 3957, 431, 1579, 6383, 9784, 5874, 677, 3336, 6234, 2766, 1323, 9115, 12237, 2031, 6956, 6413, 2281, 3969, 3991, 12133, 9522, 4737, 10996, 4774, 5429, 11871, 3772, 453, 5908, 2882, 1805, 2051, 1954, 11713, 3963, 2447, 6142, 8174, 3030, 1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796, 2057, 5369, 11939, 1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789, 5942, 10706, 10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551, 9634, 6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459, 64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065, 835, 3570, 4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922, 7967, 1958, 10211, 1112, 3728, 4049, 11130, 5990, 1404, 325, 948, 11143, 6190, 295, 11637, 5766, 8212, 8273, 2919, 8527, 6119, 6992, 8333, 1360, 2555, 6167, 1200, 7105, 7991, 3329, 9597, 12121, 5106, 5961, 10695, 10327, 3051, 9923, 4896, 9326, 81, 3091, 1000, 7969, 4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062, 2294, 3553, 4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088, 1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479, 1, 8246, 7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961, 4591, 5728, 6461, 5023, 9650, 7468, 949, 9664, 2975, 11726, 2744, 9283, 10092, 5067, 12171, 2476, 3748, 11336, 6522, 827, 9452, 5374, 12159, 7935, 3296, 3949, 9893, 4452, 10908, 2525, 3584, 8112, 8011, 10616, 4989, 6958, 11809, 9447, 12280, 1022, 11950, 9821, 11745, 5791, 5092, 2089, 9005, 2881, 3289, 2013, 9048, 729, 7901, 1260, 5755, 4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932, 9558, 8830, 3637, 5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741, 1207, 9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952, 4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302, 6022, 7278, 1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045, 2481, 5012, 7428, 354, 6591, 9377, 11847, 2401, 1067, 7188, 11516, 390, 8511, 8456, 7270, 545, 8585, 9611, 12047, 1537, 4143, 4714, 4885, 1017, 5084, 1632, 3066, 27, 1440, 8526, 9273, 12046, 11618, 9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985, 11869, 6730, 10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407, 2686, 9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863, 7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852, 12286, 4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364, 3271, 4057, 4414, 9442, 7917, 2174, 3947, 11951, 2455, 6599, 10545, 10975, 3654, 2894, 7681, 7126, 7287, 12269, 4119, 3343, 2151, 1522, 7174, 7350, 11041, 2442, 2148, 5959, 6492, 8330, 8945, 5598, 3624, 10397, 1325, 6565, 1945, 11260, 10077, 2674, 3338, 3276, 11034, 506, 6505, 1392, 5478, 8778, 1178, 2776, 3408, 10347, 11124, 2575, 9489, 12096, 6092, 10058, 4167, 6085, 923, 11251, 11912, 4578, 10669, 11914, 425, 10453, 392, 10104, 8464, 4235, 8761, 7376, 2291, 3375, 7954, 8896, 6617, 7790, 1737, 11667, 3982, 9342, 6680, 636, 6825, 7383, 512, 4670, 2900, 12050, 7735, 994, 1687, 11883, 7021, 146, 10485, 1403, 5189, 6094, 2483, 2054, 3042, 10945, 3981, 10821, 11826, 8882, 8151, 180, 9600, 7684, 5219, 10880, 6780, 204, 11232, 2600, 7584, 3121, 3017, 11053, 7814, 7043, 4251, 4739, 11063, 6771, 7073, 9261, 2360, 11925, 1928, 11825, 8024, 3678, 3205, 3359, 11197, 5209, 8581, 3238, 8840, 1136, 9363, 1826, 3171, 4489, 7885, 346, 2068, 1389, 8257, 3163, 4840, 6127, 8062, 8921, 612, 4238, 10763, 8067, 125, 11749, 10125, 5416, 2110, 716, 9839, 10584, 11475, 11873, 3448, 343, 1908, 4538, 10423, 7078, 4727, 1208, 11572, 3589, 2982, 1373, 1721, 10753, 4103, 2429, 4209, 5412, 5993, 9011, 438, 3515, 7228, 1218, 8347, 5232, 8682, 1327, 7508, 4924, 448, 1014, 10029, 12221, 4566, 5836, 12229, 2717, 1535, 3200, 5588, 5845, 412, 5102, 7326, 3744, 3056, 2528, 7406, 8314, 9202, 6454, 6613, 1417, 10032, 7784, 1518, 3765, 4176, 5063, 9828, 2275, 6636, 4267, 6463, 2065, 7725, 3495, 8328, 8755, 8144, 10533, 5966, 12077, 9175, 9520, 5596, 6302, 8400, 579, 6781, 11014, 5734, 11113, 11164, 4860, 1131, 10844, 9068, 8016, 9694, 3837, 567, 9348, 7000, 6627, 7699, 5082, 682, 11309, 5207, 4050, 7087, 844, 7434, 3769, 293, 9057, 6940, 9344, 10883, 2633, 8190, 3944, 5530, 5604, 3480, 2171, 9282, 11024, 2213, 8136, 3805, 767, 12239, 216, 11520, 6763, 10353, 7, 8566, 845, 7235, 3154, 4360, 3285, 10268, 2832, 3572, 1282, 7559, 3229, 8360, 10583, 6105, 3120, 6643, 6203, 8536, 8348, 6919, 3536, 9199, 10891, 11463, 5043, 1658, 5618, 8787, 5789, 4719, 751, 11379, 6389, 10783, 3065, 7806, 6586, 2622, 5386, 510, 7628, 6921, 578, 10345, 11839, 8929, 4684, 12226, 7154, 9916, 7302, 8481, 3670, 11066, 2334, 1590, 7878, 10734, 1802, 1891, 5103, 6151, 8820, 3418, 7846, 9951, 4693, 417, 9996, 9652, 4510, 2946, 5461, 365, 881, 1927, 1015, 11675, 11009, 1371, 12265, 2485, 11385, 5039, 6742, 8449, 1842, 12217, 8176, 9577, 4834, 7937, 9461, 2643, 11194, 3045, 6508, 4094, 3451, 7911, 11048, 5406, 4665, 3020, 6616, 11345, 7519, 3669, 5287, 1790, 7014, 5410, 11038, 11249, 2035, 6125, 10407, 4565, 7315, 5078, 10506, 2840, 2478, 9270, 4194, 9195, 4518, 7469, 1160, 6878, 2730, 10421, 10036, 1734, 3815, 10939, 5832, 10595, 10759, 4423, 8420, 9617, 7119, 11010, 11424, 9173, 189, 10080, 10526, 3466, 10588, 7592, 3578, 11511, 7785, 9663, 530, 12150, 8957, 2532, 3317, 9349, 10243, 1481, 9332, 3454, 3758, 7899, 4218, 2593, 11410, 2276, 982, 6513, 1849, 8494, 9021, 4523, 7988, 8, 457, 648, 150, 8000, 2307, 2301, 874, 5650, 170, 9462, 2873, 9855, 11498, 2535, 11169, 5808, 12268, 9687, 1901, 7171, 11787, 3846, 1573, 6063, 3793, 466, 11259, 10608, 3821, 6320, 4649, 6263, 2929]
omegas_montgomery = [4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041, 8775, 2344, 11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118, 2683, 1190, 4789, 7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973, 382, 3988, 468, 6843, 5339, 6196, 3710, 11316, 1254, 5435, 10930, 3998, 10256, 10367, 3879, 11889, 1728, 6137, 4948, 5862, 6136, 3643, 6874, 8724, 654, 10302, 1702, 7083, 6760, 56, 3199, 9987, 605, 11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689, 4080, 11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142, 241, 12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968, 12097, 7591, 5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821, 11502, 8807, 12138, 2127, 2839, 3957, 431, 1579, 6383, 9784, 5874, 677, 3336, 6234, 2766, 1323, 9115, 12237, 2031, 6956, 6413, 2281, 3969, 3991, 12133, 9522, 4737, 10996, 4774, 5429, 11871, 3772, 453, 5908, 2882, 1805, 2051, 1954, 11713, 3963, 2447, 6142, 8174, 3030, 1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796, 2057, 5369, 11939, 1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789, 5942, 10706, 10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551, 9634, 6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459, 64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065, 835, 3570, 4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922, 7967, 1958, 10211, 1112, 3728, 4049, 11130, 5990, 1404, 325, 948, 11143, 6190, 295, 11637, 5766, 8212, 8273, 2919, 8527, 6119, 6992, 8333, 1360, 2555, 6167, 1200, 7105, 7991, 3329, 9597, 12121, 5106, 5961, 10695, 10327, 3051, 9923, 4896, 9326, 81, 3091, 1000, 7969, 4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062, 2294, 3553, 4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088, 1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479, 1, 8246, 7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961, 4591, 5728, 6461, 5023, 9650, 7468, 949, 9664, 2975, 11726, 2744, 9283, 10092, 5067, 12171, 2476, 3748, 11336, 6522, 827, 9452, 5374, 12159, 7935, 3296, 3949, 9893, 4452, 10908, 2525, 3584, 8112, 8011, 10616, 4989, 6958, 11809, 9447, 12280, 1022, 11950, 9821, 11745, 5791, 5092, 2089, 9005, 2881, 3289, 2013, 9048, 729, 7901, 1260, 5755, 4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932, 9558, 8830, 3637, 5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741, 1207, 9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952, 4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302, 6022, 7278, 1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045, 2481, 5012, 7428, 354, 6591, 9377, 11847, 2401, 1067, 7188, 11516, 390, 8511, 8456, 7270, 545, 8585, 9611, 12047, 1537, 4143, 4714, 4885, 1017, 5084, 1632, 3066, 27, 1440, 8526, 9273, 12046, 11618, 9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985, 11869, 6730, 10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407, 2686, 9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863, 7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852, 12286, 4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364, 3271, 4057, 4414, 9442, 7917, 2174]
bitrev_table = [0, 512, 256, 768, 128, 640, 384, 896, 64, 576, 320, 832, 192, 704, 448, 960, 32, 544, 288, 800, 160, 672, 416, 928, 96, 608, 352, 864, 224, 736, 480, 992, 16, 528, 272, 784, 144, 656, 400, 912, 80, 592, 336, 848, 208, 720, 464, 976, 48, 560, 304, 816, 176, 688, 432, 944, 112, 624, 368, 880, 240, 752, 496, 1008, 8, 520, 264, 776, 136, 648, 392, 904, 72, 584, 328, 840, 200, 712, 456, 968, 40, 552, 296, 808, 168, 680, 424, 936, 104, 616, 360, 872, 232, 744, 488, 1000, 24, 536, 280, 792, 152, 664, 408, 920, 88, 600, 344, 856, 216, 728, 472, 984, 56, 568, 312, 824, 184, 696, 440, 952, 120, 632, 376, 888, 248, 760, 504, 1016, 4, 516, 260, 772, 132, 644, 388, 900, 68, 580, 324, 836, 196, 708, 452, 964, 36, 548, 292, 804, 164, 676, 420, 932, 100, 612, 356, 868, 228, 740, 484, 996, 20, 532, 276, 788, 148, 660, 404, 916, 84, 596, 340, 852, 212, 724, 468, 980, 52, 564, 308, 820, 180, 692, 436, 948, 116, 628, 372, 884, 244, 756, 500, 1012, 12, 524, 268, 780, 140, 652, 396, 908, 76, 588, 332, 844, 204, 716, 460, 972, 44, 556, 300, 812, 172, 684, 428, 940, 108, 620, 364, 876, 236, 748, 492, 1004, 28, 540, 284, 796, 156, 668, 412, 924, 92, 604, 348, 860, 220, 732, 476, 988, 60, 572, 316, 828, 188, 700, 444, 956, 124, 636, 380, 892, 252, 764, 508, 1020, 2, 514, 258, 770, 130, 642, 386, 898, 66, 578, 322, 834, 194, 706, 450, 962, 34, 546, 290, 802, 162, 674, 418, 930, 98, 610, 354, 866, 226, 738, 482, 994, 18, 530, 274, 786, 146, 658, 402, 914, 82, 594, 338, 850, 210, 722, 466, 978, 50, 562, 306, 818, 178, 690, 434, 946, 114, 626, 370, 882, 242, 754, 498, 1010, 10, 522, 266, 778, 138, 650, 394, 906, 74, 586, 330, 842, 202, 714, 458, 970, 42, 554, 298, 810, 170, 682, 426, 938, 106, 618, 362, 874, 234, 746, 490, 1002, 26, 538, 282, 794, 154, 666, 410, 922, 90, 602, 346, 858, 218, 730, 474, 986, 58, 570, 314, 826, 186, 698, 442, 954, 122, 634, 378, 890, 250, 762, 506, 1018, 6, 518, 262, 774, 134, 646, 390, 902, 70, 582, 326, 838, 198, 710, 454, 966, 38, 550, 294, 806, 166, 678, 422, 934, 102, 614, 358, 870, 230, 742, 486, 998, 22, 534, 278, 790, 150, 662, 406, 918, 86, 598, 342, 854, 214, 726, 470, 982, 54, 566, 310, 822, 182, 694, 438, 950, 118, 630, 374, 886, 246, 758, 502, 1014, 14, 526, 270, 782, 142, 654, 398, 910, 78, 590, 334, 846, 206, 718, 462, 974, 46, 558, 302, 814, 174, 686, 430, 942, 110, 622, 366, 878, 238, 750, 494, 1006, 30, 542, 286, 798, 158, 670, 414, 926, 94, 606, 350, 862, 222, 734, 478, 990, 62, 574, 318, 830, 190, 702, 446, 958, 126, 638, 382, 894, 254, 766, 510, 1022, 1, 513, 257, 769, 129, 641, 385, 897, 65, 577, 321, 833, 193, 705, 449, 961, 33, 545, 289, 801, 161, 673, 417, 929, 97, 609, 353, 865, 225, 737, 481, 993, 17, 529, 273, 785, 145, 657, 401, 913, 81, 593, 337, 849, 209, 721, 465, 977, 49, 561, 305, 817, 177, 689, 433, 945, 113, 625, 369, 881, 241, 753, 497, 1009, 9, 521, 265, 777, 137, 649, 393, 905, 73, 585, 329, 841, 201, 713, 457, 969, 41, 553, 297, 809, 169, 681, 425, 937, 105, 617, 361, 873, 233, 745, 489, 1001, 25, 537, 281, 793, 153, 665, 409, 921, 89, 601, 345, 857, 217, 729, 473, 985, 57, 569, 313, 825, 185, 697, 441, 953, 121, 633, 377, 889, 249, 761, 505, 1017, 5, 517, 261, 773, 133, 645, 389, 901, 69, 581, 325, 837, 197, 709, 453, 965, 37, 549, 293, 805, 165, 677, 421, 933, 101, 613, 357, 869, 229, 741, 485, 997, 21, 533, 277, 789, 149, 661, 405, 917, 85, 597, 341, 853, 213, 725, 469, 981, 53, 565, 309, 821, 181, 693, 437, 949, 117, 629, 373, 885, 245, 757, 501, 1013, 13, 525, 269, 781, 141, 653, 397, 909, 77, 589, 333, 845, 205, 717, 461, 973, 45, 557, 301, 813, 173, 685, 429, 941, 109, 621, 365, 877, 237, 749, 493, 1005, 29, 541, 285, 797, 157, 669, 413, 925, 93, 605, 349, 861, 221, 733, 477, 989, 61, 573, 317, 829, 189, 701, 445, 957, 125, 637, 381, 893, 253, 765, 509, 1021, 3, 515, 259, 771, 131, 643, 387, 899, 67, 579, 323, 835, 195, 707, 451, 963, 35, 547, 291, 803, 163, 675, 419, 931, 99, 611, 355, 867, 227, 739, 483, 995, 19, 531, 275, 787, 147, 659, 403, 915, 83, 595, 339, 851, 211, 723, 467, 979, 51, 563, 307, 819, 179, 691, 435, 947, 115, 627, 371, 883, 243, 755, 499, 1011, 11, 523, 267, 779, 139, 651, 395, 907, 75, 587, 331, 843, 203, 715, 459, 971, 43, 555, 299, 811, 171, 683, 427, 939, 107, 619, 363, 875, 235, 747, 491, 1003, 27, 539, 283, 795, 155, 667, 411, 923, 91, 603, 347, 859, 219, 731, 475, 987, 59, 571, 315, 827, 187, 699, 443, 955, 123, 635, 379, 891, 251, 763, 507, 1019, 7, 519, 263, 775, 135, 647, 391, 903, 71, 583, 327, 839, 199, 711, 455, 967, 39, 551, 295, 807, 167, 679, 423, 935, 103, 615, 359, 871, 231, 743, 487, 999, 23, 535, 279, 791, 151, 663, 407, 919, 87, 599, 343, 855, 215, 727, 471, 983, 55, 567, 311, 823, 183, 695, 439, 951, 119, 631, 375, 887, 247, 759, 503, 1015, 15, 527, 271, 783, 143, 655, 399, 911, 79, 591, 335, 847, 207, 719, 463, 975, 47, 559, 303, 815, 175, 687, 431, 943, 111, 623, 367, 879, 239, 751, 495, 1007, 31, 543, 287, 799, 159, 671, 415, 927, 95, 607, 351, 863, 223, 735, 479, 991, 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, 255, 767, 511, 1023]
omegas_inv_montgomery = [4075, 5315, 4324, 4916, 10120, 11767, 7210, 9027, 10316, 6715, 1278, 9945, 3514, 11248, 11271, 5925, 147, 8500, 7840, 6833, 5537, 4749, 4467, 7500, 11099, 9606, 6171, 8471, 8429, 5445, 11239, 7753, 9090, 12233, 5529, 5206, 10587, 1987, 11635, 3565, 5415, 8646, 6153, 6427, 7341, 6152, 10561, 400, 8410, 1922, 2033, 8291, 1359, 6854, 11035, 973, 8579, 6093, 6950, 5446, 11821, 8301, 11907, 316, 52, 3174, 10966, 9523, 6055, 8953, 11612, 6415, 2505, 5906, 10710, 11858, 8332, 9450, 10162, 151, 3482, 787, 5468, 1010, 4169, 9162, 5241, 9369, 7509, 8844, 7232, 4698, 192, 1321, 10240, 4912, 885, 6281, 10333, 7280, 8757, 11286, 58, 12048, 12147, 11184, 8812, 6608, 2844, 3438, 4212, 11314, 8687, 6068, 421, 8209, 3600, 3263, 7665, 6077, 7507, 5886, 3029, 6695, 4213, 504, 11684, 2302, 1962, 1594, 6328, 7183, 168, 2692, 8960, 4298, 5184, 11089, 6122, 9734, 10929, 3956, 5297, 6170, 3762, 9370, 4016, 4077, 6523, 652, 11994, 6099, 1146, 11341, 11964, 10885, 6299, 1159, 8240, 8561, 11177, 2078, 10331, 4322, 11367, 441, 4079, 11231, 3150, 1319, 8243, 709, 8049, 8719, 11454, 6224, 3054, 6803, 3123, 10542, 4433, 6370, 7032, 3834, 8633, 12225, 9830, 683, 1566, 5782, 9786, 9341, 12115, 723, 3009, 1693, 5735, 2655, 2738, 6421, 11942, 2925, 1975, 8532, 3315, 11863, 4754, 1858, 1583, 6347, 2500, 10800, 6374, 1483, 12240, 1263, 1815, 5383, 10777, 350, 6920, 10232, 4493, 9087, 8855, 8760, 9381, 218, 9928, 10446, 9259, 4115, 6147, 9842, 8326, 576, 10335, 10238, 10484, 9407, 6381, 11836, 8517, 418, 6860, 7515, 1293, 7552, 2767, 156, 8298, 8320, 10008, 5876, 5333, 10258, 10115, 4372, 2847, 7875, 8232, 9018, 8925, 1689, 8236, 2645, 5042, 9984, 7094, 9509, 1484, 7394, 3, 4437, 160, 3149, 113, 7370, 10123, 3915, 6998, 2704, 8653, 4938, 1426, 7635, 10512, 1663, 6957, 3510, 2370, 2865, 3978, 9320, 3247, 9603, 6882, 3186, 10659, 10163, 1153, 9405, 8241, 10040, 2178, 1544, 5559, 420, 8304, 4905, 476, 3531, 5191, 9153, 2399, 8889, 3000, 671, 243, 3016, 3763, 10849, 12262, 9223, 10657, 7205, 11272, 7404, 7575, 8146, 10752, 242, 2678, 3704, 11744, 5019, 3833, 3778, 11899, 773, 5101, 11222, 9888, 442, 2912, 5698, 11935, 4861, 7277, 9808, 11244, 2859, 3780, 11414, 4976, 10682, 7201, 8005, 11287, 5011, 6267, 2987, 2437, 3646, 2566, 10102, 9867, 6250, 5444, 2381, 11796, 8193, 4337, 11854, 1912, 1378, 404, 7644, 1065, 2143, 11121, 5277, 3248, 11082, 2548, 8058, 8907, 11934, 1759, 8582, 3694, 7110, 12144, 6747, 8652, 3459, 2731, 8357, 6378, 7399, 10861, 1696, 9863, 334, 7657, 6534, 11029, 4388, 11560, 3241, 10276, 9000, 9408, 3284, 10200, 7197, 6498, 544, 2468, 339, 11267, 9, 2842, 480, 5331, 7300, 1673, 4278, 4177, 8705, 9764, 1381, 7837, 2396, 8340, 8993, 4354, 130, 6915, 2837, 11462, 5767, 953, 8541, 9813, 118, 7222, 2197, 3006, 9545, 563, 9314, 2625, 11340, 4821, 2639, 7266, 5828, 6561, 7698, 3328, 6512, 1351, 7311, 6553, 8155, 1305, 722, 5146, 4043, 12288, 10810, 2545, 3621, 8747, 8785, 1646, 1212, 5860, 3195, 7203, 10963, 3201, 3014, 955, 11499, 9970, 11119, 3135, 3712, 7443, 9542, 7484, 8736, 9995, 11227, 1635, 9521, 1177, 8034, 140, 10436, 11563, 7678, 4320, 11289, 9198, 12208, 2963, 7393, 2366, 9238]
psis_inv_montgomery = [256, 10570, 1510, 7238, 1034, 7170, 6291, 7921, 11665, 3422, 4000, 2327, 2088, 5565, 795, 10647, 1521, 5484, 2539, 7385, 1055, 7173, 8047, 11683, 1669, 1994, 3796, 5809, 4341, 9398, 11876, 12230, 10525, 12037, 12253, 3506, 4012, 9351, 4847, 2448, 7372, 9831, 3160, 2207, 5582, 2553, 7387, 6322, 9681, 1383, 10731, 1533, 219, 5298, 4268, 7632, 6357, 9686, 8406, 4712, 9451, 10128, 4958, 5975, 11387, 8649, 11769, 6948, 11526, 12180, 1740, 10782, 6807, 2728, 7412, 4570, 4164, 4106, 11120, 12122, 8754, 11784, 3439, 5758, 11356, 6889, 9762, 11928, 1704, 1999, 10819, 12079, 12259, 7018, 11536, 1648, 1991, 2040, 2047, 2048, 10826, 12080, 8748, 8272, 8204, 1172, 1923, 7297, 2798, 7422, 6327, 4415, 7653, 6360, 11442, 12168, 7005, 8023, 9924, 8440, 8228, 2931, 7441, 1063, 3663, 5790, 9605, 10150, 1450, 8985, 11817, 10466, 10273, 12001, 3470, 7518, 1074, 1909, 7295, 9820, 4914, 702, 5367, 7789, 8135, 9940, 1420, 3714, 11064, 12114, 12264, 1752, 5517, 9566, 11900, 1700, 3754, 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