/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * Neither the name of NVIDIA CORPORATION nor the names of its * contributors may be used to endorse or promote products derived * from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* * Portions Copyright (c) 2009 Mike Giles, Oxford University. All rights * reserved. * Portions Copyright (c) 2008 Frances Y. Kuo and Stephen Joe. All rights * reserved. * * Sobol Quasi-random Number Generator example * * Based on CUDA code submitted by Mike Giles, Oxford University, United Kingdom * http://people.maths.ox.ac.uk/~gilesm/ * * and C code developed by Stephen Joe, University of Waikato, New Zealand * and Frances Kuo, University of New South Wales, Australia * http://web.maths.unsw.edu.au/~fkuo/sobol/ * * For theoretical background see: * * P. Bratley and B.L. Fox. * Implementing Sobol's quasirandom sequence generator * http://portal.acm.org/citation.cfm?id=42288 * ACM Trans. on Math. Software, 14(1):88-100, 1988 * * S. Joe and F. Kuo. * Remark on algorithm 659: implementing Sobol's quasirandom sequence generator. * http://portal.acm.org/citation.cfm?id=641879 * ACM Trans. on Math. Software, 29(1):49-57, 2003 * */ #include "sobol_primitives.h" // Each primitive is stored as a struct where // dimension is the dimension number of the polynomial (unused) // degree is the degree of the polynomial // a is a binary word representing the coefficients // m is the array of m values // The primitives are based on those generated by Stephen Joe and // Frances Kuo in the joe-kuo-6.10200 set. // c.f. http://web.maths.unsw.edu.au/~fkuo/sobol/index.html const struct primitive sobol_primitives[] = { // First dimension is a special case so this entry is actually ignored {1, 0, 0, {}}, {2, 1, 0, {1}}, {3, 2, 1, {1, 3}}, {4, 3, 1, {1, 3, 1}}, {5, 3, 2, {1, 1, 1}}, {6, 4, 1, {1, 1, 3, 3}}, {7, 4, 4, {1, 3, 5, 13}}, {8, 5, 2, {1, 1, 5, 5, 17}}, {9, 5, 4, {1, 1, 5, 5, 5}}, {10, 5, 7, {1, 1, 7, 11, 19}}, {11, 5, 11, {1, 1, 5, 1, 1}}, {12, 5, 13, {1, 1, 1, 3, 11}}, {13, 5, 14, {1, 3, 5, 5, 31}}, {14, 6, 1, {1, 3, 3, 9, 7, 49}}, {15, 6, 13, {1, 1, 1, 15, 21, 21}}, {16, 6, 16, {1, 3, 1, 13, 27, 49}}, {17, 6, 19, {1, 1, 1, 15, 7, 5}}, {18, 6, 22, {1, 3, 1, 15, 13, 25}}, {19, 6, 25, {1, 1, 5, 5, 19, 61}}, {20, 7, 1, {1, 3, 7, 11, 23, 15, 103}}, {21, 7, 4, {1, 3, 7, 13, 13, 15, 69}}, {22, 7, 7, {1, 1, 3, 13, 7, 35, 63}}, {23, 7, 8, {1, 3, 5, 9, 1, 25, 53}}, {24, 7, 14, {1, 3, 1, 13, 9, 35, 107}}, {25, 7, 19, {1, 3, 1, 5, 27, 61, 31}}, {26, 7, 21, {1, 1, 5, 11, 19, 41, 61}}, {27, 7, 28, {1, 3, 5, 3, 3, 13, 69}}, {28, 7, 31, {1, 1, 7, 13, 1, 19, 1}}, {29, 7, 32, {1, 3, 7, 5, 13, 19, 59}}, {30, 7, 37, {1, 1, 3, 9, 25, 29, 41}}, {31, 7, 41, {1, 3, 5, 13, 23, 1, 55}}, {32, 7, 42, {1, 3, 7, 3, 13, 59, 17}}, {33, 7, 50, {1, 3, 1, 3, 5, 53, 69}}, {34, 7, 55, {1, 1, 5, 5, 23, 33, 13}}, {35, 7, 56, {1, 1, 7, 7, 1, 61, 123}}, {36, 7, 59, {1, 1, 7, 9, 13, 61, 49}}, {37, 7, 62, {1, 3, 3, 5, 3, 55, 33}}, {38, 8, 14, {1, 3, 1, 15, 31, 13, 49, 245}}, {39, 8, 21, {1, 3, 5, 15, 31, 59, 63, 97}}, {40, 8, 22, {1, 3, 1, 11, 11, 11, 77, 249}}, {41, 8, 38, {1, 3, 1, 11, 27, 43, 71, 9}}, {42, 8, 47, {1, 1, 7, 15, 21, 11, 81, 45}}, {43, 8, 49, {1, 3, 7, 3, 25, 31, 65, 79}}, {44, 8, 50, {1, 3, 1, 1, 19, 11, 3, 205}}, {45, 8, 52, {1, 1, 5, 9, 19, 21, 29, 157}}, {46, 8, 56, {1, 3, 7, 11, 1, 33, 89, 185}}, {47, 8, 67, {1, 3, 3, 3, 15, 9, 79, 71}}, {48, 8, 70, {1, 3, 7, 11, 15, 39, 119, 27}}, {49, 8, 84, {1, 1, 3, 1, 11, 31, 97, 225}}, {50, 8, 97, {1, 1, 1, 3, 23, 43, 57, 177}}, {51, 8, 103, {1, 3, 7, 7, 17, 17, 37, 71}}, {52, 8, 115, {1, 3, 1, 5, 27, 63, 123, 213}}, {53, 8, 122, {1, 1, 3, 5, 11, 43, 53, 133}}, {54, 9, 8, {1, 3, 5, 5, 29, 17, 47, 173, 479}}, {55, 9, 13, {1, 3, 3, 11, 3, 1, 109, 9, 69}}, {56, 9, 16, {1, 1, 1, 5, 17, 39, 23, 5, 343}}, {57, 9, 22, {1, 3, 1, 5, 25, 15, 31, 103, 499}}, {58, 9, 25, {1, 1, 1, 11, 11, 17, 63, 105, 183}}, {59, 9, 44, {1, 1, 5, 11, 9, 29, 97, 231, 363}}, {60, 9, 47, {1, 1, 5, 15, 19, 45, 41, 7, 383}}, {61, 9, 52, {1, 3, 7, 7, 31, 19, 83, 137, 221}}, {62, 9, 55, {1, 1, 1, 3, 23, 15, 111, 223, 83}}, {63, 9, 59, {1, 1, 5, 13, 31, 15, 55, 25, 161}}, {64, 9, 62, {1, 1, 3, 13, 25, 47, 39, 87, 257}}, {65, 9, 67, {1, 1, 1, 11, 21, 53, 125, 249, 293}}, {66, 9, 74, {1, 1, 7, 11, 11, 7, 57, 79, 323}}, {67, 9, 81, {1, 1, 5, 5, 17, 13, 81, 3, 131}}, {68, 9, 82, {1, 1, 7, 13, 23, 7, 65, 251, 475}}, {69, 9, 87, {1, 3, 5, 1, 9, 43, 3, 149, 11}}, {70, 9, 91, {1, 1, 3, 13, 31, 13, 13, 255, 487}}, {71, 9, 94, {1, 3, 3, 1, 5, 63, 89, 91, 127}}, {72, 9, 103, {1, 1, 3, 3, 1, 19, 123, 127, 237}}, {73, 9, 104, {1, 1, 5, 7, 23, 31, 37, 243, 289}}, {74, 9, 109, {1, 1, 5, 11, 17, 53, 117, 183, 491}}, {75, 9, 122, {1, 1, 1, 5, 1, 13, 13, 209, 345}}, {76, 9, 124, {1, 1, 3, 15, 1, 57, 115, 7, 33}}, {77, 9, 137, {1, 3, 1, 11, 7, 43, 81, 207, 175}}, {78, 9, 138, {1, 3, 1, 1, 15, 27, 63, 255, 49}}, {79, 9, 143, {1, 3, 5, 3, 27, 61, 105, 171, 305}}, {80, 9, 145, {1, 1, 5, 3, 1, 3, 57, 249, 149}}, {81, 9, 152, {1, 1, 3, 5, 5, 57, 15, 13, 159}}, {82, 9, 157, {1, 1, 1, 11, 7, 11, 105, 141, 225}}, {83, 9, 167, {1, 3, 3, 5, 27, 59, 121, 101, 271}}, {84, 9, 173, {1, 3, 5, 9, 11, 49, 51, 59, 115}}, {85, 9, 176, {1, 1, 7, 1, 23, 45, 125, 71, 419}}, {86, 9, 181, {1, 1, 3, 5, 23, 5, 105, 109, 75}}, {87, 9, 182, {1, 1, 7, 15, 7, 11, 67, 121, 453}}, {88, 9, 185, {1, 3, 7, 3, 9, 13, 31, 27, 449}}, {89, 9, 191, {1, 3, 1, 15, 19, 39, 39, 89, 15}}, {90, 9, 194, {1, 1, 1, 1, 1, 33, 73, 145, 379}}, {91, 9, 199, {1, 3, 1, 15, 15, 43, 29, 13, 483}}, {92, 9, 218, {1, 1, 7, 3, 19, 27, 85, 131, 431}}, {93, 9, 220, {1, 3, 3, 3, 5, 35, 23, 195, 349}}, {94, 9, 227, {1, 3, 3, 7, 9, 27, 39, 59, 297}}, {95, 9, 229, {1, 1, 3, 9, 11, 17, 13, 241, 157}}, {96, 9, 230, {1, 3, 7, 15, 25, 57, 33, 189, 213}}, {97, 9, 234, {1, 1, 7, 1, 9, 55, 73, 83, 217}}, {98, 9, 236, {1, 3, 3, 13, 19, 27, 23, 113, 249}}, {99, 9, 241, {1, 3, 5, 3, 23, 43, 3, 253, 479}}, {100, 9, 244, {1, 1, 5, 5, 11, 5, 45, 117, 217}}, {101, 9, 253, {1, 3, 3, 7, 29, 37, 33, 123, 147}}, {102, 10, 4, {1, 3, 1, 15, 5, 5, 37, 227, 223, 459}}, {103, 10, 13, {1, 1, 7, 5, 5, 39, 63, 255, 135, 487}}, {104, 10, 19, {1, 3, 1, 7, 9, 7, 87, 249, 217, 599}}, {105, 10, 22, {1, 1, 3, 13, 9, 47, 7, 225, 363, 247}}, {106, 10, 50, {1, 3, 7, 13, 19, 13, 9, 67, 9, 737}}, {107, 10, 55, {1, 3, 5, 5, 19, 59, 7, 41, 319, 677}}, {108, 10, 64, {1, 1, 5, 3, 31, 63, 15, 43, 207, 789}}, {109, 10, 69, {1, 1, 7, 9, 13, 39, 3, 47, 497, 169}}, {110, 10, 98, {1, 3, 1, 7, 21, 17, 97, 19, 415, 905}}, {111, 10, 107, {1, 3, 7, 1, 3, 31, 71, 111, 165, 127}}, {112, 10, 115, {1, 1, 5, 11, 1, 61, 83, 119, 203, 847}}, {113, 10, 121, {1, 3, 3, 13, 9, 61, 19, 97, 47, 35}}, {114, 10, 127, {1, 1, 7, 7, 15, 29, 63, 95, 417, 469}}, {115, 10, 134, {1, 3, 1, 9, 25, 9, 71, 57, 213, 385}}, {116, 10, 140, {1, 3, 5, 13, 31, 47, 101, 57, 39, 341}}, {117, 10, 145, {1, 1, 3, 3, 31, 57, 125, 173, 365, 551}}, {118, 10, 152, {1, 3, 7, 1, 13, 57, 67, 157, 451, 707}}, {119, 10, 158, {1, 1, 1, 7, 21, 13, 105, 89, 429, 965}}, {120, 10, 161, {1, 1, 5, 9, 17, 51, 45, 119, 157, 141}}, {121, 10, 171, {1, 3, 7, 7, 13, 45, 91, 9, 129, 741}}, {122, 10, 181, {1, 3, 7, 1, 23, 57, 67, 141, 151, 571}}, {123, 10, 194, {1, 1, 3, 11, 17, 47, 93, 107, 375, 157}}, {124, 10, 199, {1, 3, 3, 5, 11, 21, 43, 51, 169, 915}}, {125, 10, 203, {1, 1, 5, 3, 15, 55, 101, 67, 455, 625}}, {126, 10, 208, {1, 3, 5, 9, 1, 23, 29, 47, 345, 595}}, {127, 10, 227, {1, 3, 7, 7, 5, 49, 29, 155, 323, 589}}, {128, 10, 242, {1, 3, 3, 7, 5, 41, 127, 61, 261, 717}}, {129, 10, 251, {1, 3, 7, 7, 17, 23, 117, 67, 129, 1009}}, {130, 10, 253, {1, 1, 3, 13, 11, 39, 21, 207, 123, 305}}, {131, 10, 265, {1, 1, 3, 9, 29, 3, 95, 47, 231, 73}}, {132, 10, 266, {1, 3, 1, 9, 1, 29, 117, 21, 441, 259}}, {133, 10, 274, {1, 3, 1, 13, 21, 39, 125, 211, 439, 723}}, {134, 10, 283, {1, 1, 7, 3, 17, 63, 115, 89, 49, 773}}, {135, 10, 289, {1, 3, 7, 13, 11, 33, 101, 107, 63, 73}}, {136, 10, 295, {1, 1, 5, 5, 13, 57, 63, 135, 437, 177}}, {137, 10, 301, {1, 1, 3, 7, 27, 63, 93, 47, 417, 483}}, {138, 10, 316, {1, 1, 3, 1, 23, 29, 1, 191, 49, 23}}, {139, 10, 319, {1, 1, 3, 15, 25, 55, 9, 101, 219, 607}}, {140, 10, 324, {1, 3, 1, 7, 7, 19, 51, 251, 393, 307}}, {141, 10, 346, {1, 3, 3, 3, 25, 55, 17, 75, 337, 3}}, {142, 10, 352, {1, 1, 1, 13, 25, 17, 65, 45, 479, 413}}, {143, 10, 361, {1, 1, 7, 7, 27, 49, 99, 161, 213, 727}}, {144, 10, 367, {1, 3, 5, 1, 23, 5, 43, 41, 251, 857}}, {145, 10, 382, {1, 3, 3, 7, 11, 61, 39, 87, 383, 835}}, {146, 10, 395, {1, 1, 3, 15, 13, 7, 29, 7, 505, 923}}, {147, 10, 398, {1, 3, 7, 1, 5, 31, 47, 157, 445, 501}}, {148, 10, 400, {1, 1, 3, 7, 1, 43, 9, 147, 115, 605}}, {149, 10, 412, {1, 3, 3, 13, 5, 1, 119, 211, 455, 1001}}, {150, 10, 419, {1, 1, 3, 5, 13, 19, 3, 243, 75, 843}}, {151, 10, 422, {1, 3, 7, 7, 1, 19, 91, 249, 357, 589}}, {152, 10, 426, {1, 1, 1, 9, 1, 25, 109, 197, 279, 411}}, {153, 10, 428, {1, 3, 1, 15, 23, 57, 59, 135, 191, 75}}, {154, 10, 433, {1, 1, 5, 15, 29, 21, 39, 253, 383, 349}}, {155, 10, 446, {1, 3, 3, 5, 19, 45, 61, 151, 199, 981}}, {156, 10, 454, {1, 3, 5, 13, 9, 61, 107, 141, 141, 1}}, {157, 10, 457, {1, 3, 1, 11, 27, 25, 85, 105, 309, 979}}, {158, 10, 472, {1, 3, 3, 11, 19, 7, 115, 223, 349, 43}}, {159, 10, 493, {1, 1, 7, 9, 21, 39, 123, 21, 275, 927}}, {160, 10, 505, {1, 1, 7, 13, 15, 41, 47, 243, 303, 437}}, {161, 10, 508, {1, 1, 1, 7, 7, 3, 15, 99, 409, 719}}, {162, 11, 2, {1, 3, 3, 15, 27, 49, 113, 123, 113, 67, 469}}, {163, 11, 11, {1, 3, 7, 11, 3, 23, 87, 169, 119, 483, 199}}, {164, 11, 21, {1, 1, 5, 15, 7, 17, 109, 229, 179, 213, 741}}, {165, 11, 22, {1, 1, 5, 13, 11, 17, 25, 135, 403, 557, 1433}}, {166, 11, 35, {1, 3, 1, 1, 1, 61, 67, 215, 189, 945, 1243}}, {167, 11, 49, {1, 1, 7, 13, 17, 33, 9, 221, 429, 217, 1679}}, {168, 11, 50, {1, 1, 3, 11, 27, 3, 15, 93, 93, 865, 1049}}, {169, 11, 56, {1, 3, 7, 7, 25, 41, 121, 35, 373, 379, 1547}}, {170, 11, 61, {1, 3, 3, 9, 11, 35, 45, 205, 241, 9, 59}}, {171, 11, 70, {1, 3, 1, 7, 3, 51, 7, 177, 53, 975, 89}}, {172, 11, 74, {1, 1, 3, 5, 27, 1, 113, 231, 299, 759, 861}}, {173, 11, 79, {1, 3, 3, 15, 25, 29, 5, 255, 139, 891, 2031}}, {174, 11, 84, {1, 3, 1, 1, 13, 9, 109, 193, 419, 95, 17}}, {175, 11, 88, {1, 1, 7, 9, 3, 7, 29, 41, 135, 839, 867}}, {176, 11, 103, {1, 1, 7, 9, 25, 49, 123, 217, 113, 909, 215}}, {177, 11, 104, {1, 1, 7, 3, 23, 15, 43, 133, 217, 327, 901}}, {178, 11, 112, {1, 1, 3, 3, 13, 53, 63, 123, 477, 711, 1387}}, {179, 11, 115, {1, 1, 3, 15, 7, 29, 75, 119, 181, 957, 247}}, {180, 11, 117, {1, 1, 1, 11, 27, 25, 109, 151, 267, 99, 1461}}, {181, 11, 122, {1, 3, 7, 15, 5, 5, 53, 145, 11, 725, 1501}}, {182, 11, 134, {1, 3, 7, 1, 9, 43, 71, 229, 157, 607, 1835}}, {183, 11, 137, {1, 3, 3, 13, 25, 1, 5, 27, 471, 349, 127}}, {184, 11, 146, {1, 1, 1, 1, 23, 37, 9, 221, 269, 897, 1685}}, {185, 11, 148, {1, 1, 3, 3, 31, 29, 51, 19, 311, 553, 1969}}, {186, 11, 157, {1, 3, 7, 5, 5, 55, 17, 39, 475, 671, 1529}}, {187, 11, 158, {1, 1, 7, 1, 1, 35, 47, 27, 437, 395, 1635}}, {188, 11, 162, {1, 1, 7, 3, 13, 23, 43, 135, 327, 139, 389}}, {189, 11, 164, {1, 3, 7, 3, 9, 25, 91, 25, 429, 219, 513}}, {190, 11, 168, {1, 1, 3, 5, 13, 29, 119, 201, 277, 157, 2043}}, {191, 11, 173, {1, 3, 5, 3, 29, 57, 13, 17, 167, 739, 1031}}, {192, 11, 185, {1, 3, 3, 5, 29, 21, 95, 27, 255, 679, 1531}}, {193, 11, 186, {1, 3, 7, 15, 9, 5, 21, 71, 61, 961, 1201}}, {194, 11, 191, {1, 3, 5, 13, 15, 57, 33, 93, 459, 867, 223}}, {195, 11, 193, {1, 1, 1, 15, 17, 43, 127, 191, 67, 177, 1073}}, {196, 11, 199, {1, 1, 1, 15, 23, 7, 21, 199, 75, 293, 1611}}, {197, 11, 213, {1, 3, 7, 13, 15, 39, 21, 149, 65, 741, 319}}, {198, 11, 214, {1, 3, 7, 11, 23, 13, 101, 89, 277, 519, 711}}, {199, 11, 220, {1, 3, 7, 15, 19, 27, 85, 203, 441, 97, 1895}}, {200, 11, 227, {1, 3, 1, 3, 29, 25, 21, 155, 11, 191, 197}}, {201, 11, 236, {1, 1, 7, 5, 27, 11, 81, 101, 457, 675, 1687}}, {202, 11, 242, {1, 3, 1, 5, 25, 5, 65, 193, 41, 567, 781}}, {203, 11, 251, {1, 3, 1, 5, 11, 15, 113, 77, 411, 695, 1111}}, {204, 11, 256, {1, 1, 3, 9, 11, 53, 119, 171, 55, 297, 509}}, {205, 11, 259, {1, 1, 1, 1, 11, 39, 113, 139, 165, 347, 595}}, {206, 11, 265, {1, 3, 7, 11, 9, 17, 101, 13, 81, 325, 1733}}, {207, 11, 266, {1, 3, 1, 1, 21, 43, 115, 9, 113, 907, 645}}, {208, 11, 276, {1, 1, 7, 3, 9, 25, 117, 197, 159, 471, 475}}, {209, 11, 292, {1, 3, 1, 9, 11, 21, 57, 207, 485, 613, 1661}}, {210, 11, 304, {1, 1, 7, 7, 27, 55, 49, 223, 89, 85, 1523}}, {211, 11, 310, {1, 1, 5, 3, 19, 41, 45, 51, 447, 299, 1355}}, {212, 11, 316, {1, 3, 1, 15, 1, 35, 119, 135, 427, 93, 1311}}, {213, 11, 319, {1, 3, 1, 15, 31, 39, 121, 145, 129, 903, 333}}, {214, 11, 322, {1, 1, 5, 3, 29, 7, 9, 11, 395, 119, 873}}, {215, 11, 328, {1, 3, 5, 11, 27, 29, 5, 117, 469, 31, 1811}}, {216, 11, 334, {1, 1, 7, 15, 21, 25, 71, 15, 89, 1021, 679}}, {217, 11, 339, {1, 3, 7, 9, 21, 39, 51, 111, 327, 809, 845}}, {218, 11, 341, {1, 3, 3, 13, 3, 33, 79, 17, 183, 599, 1859}}, {219, 11, 345, {1, 1, 7, 9, 31, 9, 1, 5, 353, 395, 833}}, {220, 11, 346, {1, 3, 5, 7, 3, 53, 81, 133, 155, 355, 1559}}, {221, 11, 362, {1, 3, 5, 5, 31, 13, 89, 195, 357, 769, 889}}, {222, 11, 367, {1, 1, 7, 1, 9, 21, 77, 31, 269, 857, 923}}, {223, 11, 372, {1, 1, 1, 11, 11, 27, 61, 185, 329, 685, 325}}, {224, 11, 375, {1, 1, 1, 5, 11, 31, 71, 79, 293, 29, 17}}, {225, 11, 376, {1, 1, 7, 7, 7, 41, 65, 167, 67, 153, 1305}}, {226, 11, 381, {1, 3, 3, 5, 23, 45, 109, 205, 191, 649, 749}}, {227, 11, 385, {1, 1, 7, 7, 17, 1, 73, 211, 19, 797, 1009}}, {228, 11, 388, {1, 1, 5, 9, 23, 15, 117, 213, 183, 477, 1301}}, {229, 11, 392, {1, 1, 5, 13, 23, 35, 55, 151, 267, 883, 1479}}, {230, 11, 409, {1, 1, 1, 7, 5, 43, 77, 11, 149, 297, 329}}, {231, 11, 415, {1, 1, 7, 15, 3, 41, 55, 123, 219, 499, 377}}, {232, 11, 416, {1, 3, 3, 1, 27, 7, 113, 141, 173, 379, 1087}}, {233, 11, 421, {1, 3, 1, 9, 7, 25, 45, 49, 415, 329, 483}}, {234, 11, 428, {1, 1, 7, 7, 7, 15, 75, 191, 305, 757, 813}}, {235, 11, 431, {1, 3, 7, 5, 31, 15, 21, 247, 29, 297, 1015}}, {236, 11, 434, {1, 3, 1, 13, 3, 41, 69, 235, 431, 515, 1889}}, {237, 11, 439, {1, 1, 5, 7, 31, 5, 69, 193, 229, 439, 1043}}, {238, 11, 446, {1, 3, 5, 13, 31, 33, 45, 159, 477, 707, 1605}}, {239, 11, 451, {1, 1, 1, 7, 23, 49, 107, 223, 7, 429, 2047}}, {240, 11, 453, {1, 3, 5, 1, 31, 17, 117, 133, 331, 97, 833}}, {241, 11, 457, {1, 3, 1, 11, 7, 31, 103, 5, 299, 601, 981}}, {242, 11, 458, {1, 3, 5, 5, 15, 57, 87, 39, 217, 155, 361}}, {243, 11, 471, {1, 1, 7, 15, 29, 19, 125, 131, 37, 635, 1429}}, {244, 11, 475, {1, 3, 1, 9, 29, 3, 59, 107, 341, 809, 101}}, {245, 11, 478, {1, 1, 5, 15, 9, 37, 113, 225, 139, 165, 393}}, {246, 11, 484, {1, 3, 3, 13, 27, 21, 35, 255, 189, 45, 103}}, {247, 11, 493, {1, 1, 7, 5, 7, 59, 39, 87, 319, 723, 955}}, {248, 11, 494, {1, 3, 1, 1, 9, 23, 83, 47, 413, 445, 787}}, {249, 11, 499, {1, 3, 3, 3, 9, 27, 113, 135, 279, 915, 1221}}, {250, 11, 502, {1, 3, 7, 15, 3, 49, 99, 67, 11, 1017, 891}}, {251, 11, 517, {1, 3, 1, 9, 31, 41, 9, 205, 39, 993, 105}}, {252, 11, 518, {1, 3, 3, 7, 11, 45, 67, 123, 303, 87, 1943}}, {253, 11, 524, {1, 1, 1, 9, 1, 51, 101, 253, 499, 879, 833}}, {254, 11, 527, {1, 3, 7, 15, 19, 51, 97, 13, 499, 231, 829}}, {255, 11, 555, 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3, 3, 15, 37, 23, 31, 169, 321, 25, 3637, 1129, 12461, 4741}}, {1874, 15, 59, {1, 3, 3, 11, 5, 63, 57, 55, 65, 715, 307, 2315, 3725, 13937, 29497}}, {1875, 15, 64, {1, 1, 7, 5, 7, 41, 53, 115, 391, 1011, 201, 1069, 7425, 9775, 25067}}, {1876, 15, 67, {1, 1, 7, 7, 3, 39, 87, 139, 253, 405, 2007, 3489, 395, 10591, 21825}}, {1877, 15, 73, {1, 1, 3, 9, 23, 55, 51, 193, 91, 617, 943, 81, 1249, 14799, 24349}}, {1878, 15, 82, {1, 3, 7, 7, 17, 35, 27, 173, 169, 867, 1833, 905, 8095, 12045, 21097}}, {1879, 15, 97, {1, 1, 1, 7, 5, 45, 17, 73, 389, 335, 1481, 2339, 1403, 13291, 1967}}, {1880, 15, 103, {1, 3, 1, 5, 19, 13, 123, 63, 321, 259, 581, 1475, 7995, 6321, 30781}}, {1881, 15, 110, {1, 1, 7, 3, 9, 21, 69, 13, 151, 611, 1129, 1743, 5423, 16339, 12699}}, {1882, 15, 115, {1, 1, 3, 3, 13, 33, 23, 243, 293, 793, 213, 2909, 5681, 16143, 24717}}, {1883, 15, 122, {1, 3, 1, 13, 17, 19, 95, 33, 371, 207, 633, 43, 5313, 5585, 10767}}, {1884, 15, 128, {1, 1, 5, 13, 17, 11, 123, 19, 45, 855, 243, 1267, 2115, 3255, 28091}}, {1885, 15, 138, {1, 3, 7, 15, 21, 45, 7, 13, 481, 29, 969, 1415, 7941, 4409, 17327}}, {1886, 15, 146, {1, 1, 5, 11, 7, 43, 83, 175, 127, 41, 1561, 471, 3949, 9773, 27339}}, {1887, 15, 171, {1, 1, 7, 11, 31, 47, 95, 183, 137, 27, 1743, 2983, 5123, 8705, 10745}}, {1888, 15, 174, {1, 1, 5, 5, 5, 39, 9, 89, 363, 957, 1251, 2731, 3991, 13595, 21205}}, {1889, 15, 176, {1, 1, 1, 9, 3, 43, 103, 29, 205, 323, 1843, 13, 3943, 5819, 12421}}, {1890, 15, 182, {1, 1, 7, 9, 19, 47, 53, 85, 225, 651, 799, 2593, 7241, 14981, 20391}}, {1891, 15, 194, {1, 1, 5, 15, 29, 45, 65, 211, 337, 273, 1761, 1875, 1123, 12069, 3169}}, {1892, 15, 208, {1, 3, 1, 11, 21, 45, 1, 41, 339, 441, 1799, 1271, 6161, 13081, 24991}}, {1893, 15, 211, {1, 3, 3, 3, 21, 47, 87, 207, 465, 899, 1555, 1591, 7855, 10701, 26791}}, {1894, 15, 220, {1, 1, 1, 5, 1, 5, 33, 77, 477, 747, 201, 3095, 555, 7685, 6129}}, {1895, 15, 229, {1, 3, 1, 11, 13, 7, 65, 87, 391, 699, 913, 3799, 5441, 14025, 26153}}, {1896, 15, 230, {1, 1, 5, 7, 27, 17, 101, 149, 233, 711, 1761, 1257, 8081, 12103, 10781}}, {1897, 15, 239, {1, 1, 3, 1, 27, 3, 63, 189, 309, 513, 1757, 3311, 4761, 57, 6305}}, {1898, 15, 254, {1, 3, 3, 1, 13, 55, 49, 171, 5, 61, 39, 723, 7835, 15009, 3845}}, {1899, 15, 265, {1, 1, 1, 11, 1, 7, 123, 145, 307, 873, 739, 1491, 8141, 11489, 9165}}, {1900, 15, 285, {1, 3, 3, 5, 9, 5, 123, 57, 31, 289, 1735, 1255, 411, 15865, 5527}}, {1901, 15, 290, {1, 1, 5, 9, 3, 37, 125, 245, 355, 433, 1791, 3793, 6867, 15237, 5821}}, {1902, 15, 319, {1, 3, 3, 1, 9, 35, 115, 117, 331, 41, 1489, 3919, 8101, 14171, 9519}}, {1903, 15, 324, {1, 3, 1, 15, 27, 27, 45, 99, 21, 333, 1017, 791, 5641, 7839, 23597}}, {1904, 15, 327, {1, 1, 7, 9, 5, 45, 85, 239, 333, 959, 519, 3655, 2597, 155, 24489}}, {1905, 15, 333, {1, 1, 5, 7, 27, 11, 1, 103, 251, 967, 1625, 1029, 3833, 12345, 11181}}, {1906, 15, 357, {1, 1, 5, 13, 5, 33, 101, 163, 27, 669, 17, 873, 1025, 4237, 24849}}, {1907, 15, 364, {1, 1, 3, 3, 7, 25, 125, 17, 361, 57, 625, 2183, 4861, 8631, 16519}}, {1908, 15, 395, {1, 3, 7, 15, 25, 43, 125, 23, 297, 277, 717, 1927, 5833, 13949, 27595}}, {1909, 15, 397, {1, 3, 5, 13, 3, 7, 69, 43, 387, 69, 1851, 3639, 4755, 15749, 2291}}, {1910, 15, 405, {1, 3, 1, 11, 13, 3, 39, 201, 143, 973, 1827, 2861, 5561, 539, 18273}}, {1911, 15, 409, {1, 3, 5, 11, 27, 23, 77, 95, 507, 175, 967, 515, 3341, 15073, 1631}}, {1912, 15, 419, {1, 3, 5, 1, 13, 31, 83, 241, 225, 123, 1369, 1565, 4933, 13565, 29297}}, {1913, 15, 422, {1, 3, 1, 13, 19, 51, 53, 41, 37, 135, 811, 1239, 897, 11643, 389}}, {1914, 15, 431, {1, 3, 3, 13, 23, 27, 87, 23, 67, 325, 2025, 521, 6699, 2343, 13291}}, {1915, 15, 433, {1, 1, 1, 7, 11, 9, 19, 231, 339, 37, 1615, 3715, 7081, 8959, 25735}}, {1916, 15, 436, {1, 3, 5, 9, 15, 57, 15, 75, 135, 507, 1723, 3053, 4565, 10735, 5229}}, {1917, 15, 440, {1, 3, 3, 7, 21, 57, 27, 157, 351, 633, 639, 1755, 7903, 4655, 29409}}, {1918, 15, 453, {1, 1, 7, 3, 1, 41, 7, 209, 227, 1003, 1089, 3655, 2055, 6321, 14603}}, {1919, 15, 460, {1, 1, 3, 5, 17, 41, 13, 229, 231, 277, 15, 3337, 4697, 7249, 21153}}, {1920, 15, 471, {1, 3, 3, 1, 15, 57, 21, 21, 359, 821, 149, 2155, 5725, 2833, 29503}}, {1921, 15, 478, {1, 3, 7, 7, 11, 29, 37, 103, 201, 453, 2033, 3273, 3369, 15017, 27613}}, {1922, 15, 482, {1, 3, 3, 15, 19, 19, 119, 139, 475, 673, 1061, 849, 1885, 6431, 7261}}, {1923, 15, 488, {1, 3, 7, 13, 15, 29, 63, 89, 207, 461, 25, 551, 3227, 491, 20345}}, {1924, 15, 524, {1, 1, 7, 15, 31, 29, 31, 193, 181, 533, 1083, 837, 97, 4903, 26167}}, {1925, 15, 529, {1, 3, 5, 15, 13, 13, 53, 197, 73, 49, 373, 3933, 195, 2979, 29091}}, {1926, 15, 535, {1, 1, 5, 5, 23, 33, 35, 69, 115, 203, 141, 3627, 7265, 11755, 31243}}, {1927, 15, 536, {1, 1, 5, 11, 13, 19, 9, 205, 31, 69, 1711, 3183, 2149, 3137, 13631}}, {1928, 15, 539, {1, 3, 7, 5, 25, 1, 105, 47, 93, 781, 277, 1717, 6543, 14741, 25523}}, {1929, 15, 563, {1, 1, 1, 3, 27, 45, 25, 229, 215, 897, 115, 863, 7575, 14219, 22019}}, {1930, 15, 566, {1, 3, 5, 1, 3, 31, 107, 161, 303, 43, 1839, 2139, 6697, 12223, 1923}}, {1931, 15, 572, {1, 3, 3, 3, 1, 45, 11, 51, 145, 233, 517, 2927, 5821, 2931, 20693}}, {1932, 15, 577, {1, 1, 1, 3, 23, 63, 73, 99, 27, 161, 507, 2865, 3613, 9359, 9027}}, {1933, 15, 587, {1, 1, 5, 9, 29, 55, 127, 101, 17, 795, 1713, 1749, 5195, 8609, 24111}}, {1934, 15, 592, {1, 3, 1, 1, 3, 29, 33, 25, 69, 715, 1847, 2283, 1225, 1131, 30285}}, {1935, 15, 602, {1, 3, 5, 5, 3, 11, 37, 189, 381, 879, 1565, 2163, 1327, 9945, 28539}}, {1936, 15, 623, {1, 1, 5, 11, 3, 55, 3, 51, 25, 777, 1749, 75, 409, 6485, 27585}}, {1937, 15, 635, {1, 3, 3, 9, 19, 53, 43, 199, 207, 207, 825, 1867, 4947, 8507, 30483}}, {1938, 15, 638, {1, 1, 1, 1, 9, 31, 29, 65, 413, 37, 187, 2373, 321, 7199, 14443}}, {1939, 15, 654, {1, 3, 3, 11, 31, 27, 47, 7, 325, 333, 271, 3689, 1897, 12775, 25993}}, {1940, 15, 656, {1, 1, 5, 5, 5, 39, 119, 117, 329, 475, 331, 2429, 1803, 4849, 915}}, {1941, 15, 659, {1, 1, 7, 5, 19, 35, 45, 107, 327, 489, 1235, 1693, 6463, 603, 31655}}, {1942, 15, 665, {1, 3, 7, 9, 17, 37, 89, 187, 57, 201, 999, 797, 5317, 3609, 13877}}, {1943, 15, 675, {1, 1, 1, 11, 19, 21, 15, 131, 47, 5, 187, 2353, 3739, 11951, 22283}}, {1944, 15, 677, {1, 1, 1, 7, 7, 1, 41, 213, 205, 333, 2029, 1983, 7039, 6241, 16941}}, {1945, 15, 687, {1, 3, 1, 5, 7, 37, 83, 115, 199, 125, 509, 2535, 7441, 8157, 8921}}, {1946, 15, 696, {1, 3, 5, 13, 29, 35, 13, 221, 457, 707, 1001, 3585, 2301, 10283, 26081}}, {1947, 15, 701, {1, 1, 3, 3, 11, 1, 103, 93, 153, 277, 1705, 1403, 2877, 741, 22913}}, {1948, 15, 704, {1, 3, 7, 3, 3, 47, 35, 251, 309, 323, 1159, 895, 3407, 6507, 4677}}, {1949, 15, 710, {1, 3, 7, 15, 11, 13, 45, 51, 53, 833, 137, 1409, 7043, 4067, 13939}}, {1950, 15, 721, {1, 1, 3, 11, 21, 39, 71, 25, 197, 645, 501, 3119, 1053, 7855, 30873}}, {1951, 15, 728, {1, 3, 5, 15, 29, 51, 93, 31, 387, 785, 167, 3815, 5477, 4255, 17975}}, {1952, 15, 738, {1, 1, 1, 3, 1, 33, 93, 9, 49, 389, 2009, 4095, 6299, 4451, 18043}}, {1953, 15, 740, {1, 3, 5, 15, 13, 43, 43, 167, 361, 445, 1685, 3677, 3901, 5693, 18901}}, {1954, 15, 749, {1, 1, 3, 9, 1, 11, 55, 61, 65, 515, 1723, 1235, 1613, 15083, 9529}}, {1955, 15, 758, {1, 1, 3, 5, 31, 23, 107, 169, 109, 1005, 195, 3509, 4879, 15767, 23089}}, {1956, 15, 761, {1, 3, 7, 11, 3, 35, 61, 117, 99, 311, 1909, 2329, 3499, 8701, 27507}}, {1957, 15, 772, {1, 3, 7, 11, 1, 21, 27, 167, 77, 469, 2045, 873, 3441, 7377, 6225}}, {1958, 15, 776, {1, 1, 5, 3, 19, 17, 97, 55, 43, 17, 577, 765, 4027, 9511, 28643}}, {1959, 15, 782, {1, 3, 5, 7, 31, 47, 71, 41, 109, 441, 815, 1483, 6881, 595, 7263}}, {1960, 15, 789, {1, 1, 3, 9, 21, 63, 109, 231, 303, 381, 1701, 2877, 6899, 967, 30047}}, {1961, 15, 810, {1, 3, 5, 1, 19, 31, 21, 201, 167, 649, 823, 715, 2289, 5081, 14869}}, {1962, 15, 812, {1, 1, 7, 13, 23, 23, 59, 217, 263, 213, 1495, 2915, 2237, 1669, 14415}}, {1963, 15, 818, {1, 1, 3, 7, 29, 53, 109, 57, 429, 55, 573, 3529, 7687, 13853, 27299}}, {1964, 15, 830, {1, 3, 5, 3, 23, 13, 107, 99, 81, 483, 411, 223, 2907, 5095, 28383}}, {1965, 15, 832, {1, 1, 1, 5, 25, 29, 125, 233, 107, 381, 291, 3781, 1127, 5987, 11707}}, {1966, 15, 852, {1, 3, 7, 13, 29, 49, 17, 209, 379, 89, 1939, 1981, 129, 10907, 21123}}, {1967, 15, 855, {1, 3, 5, 15, 25, 37, 93, 81, 359, 675, 2039, 685, 2405, 6439, 22425}}, {1968, 15, 859, {1, 3, 3, 7, 3, 25, 43, 179, 233, 167, 1969, 537, 2781, 9605, 2411}}, {1969, 15, 865, {1, 3, 7, 13, 9, 49, 81, 195, 213, 593, 163, 707, 3887, 4557, 1051}}, {1970, 15, 877, {1, 3, 5, 13, 3, 47, 5, 197, 341, 1015, 1699, 35, 6907, 11365, 15213}}, {1971, 15, 895, {1, 3, 3, 11, 27, 13, 109, 127, 13, 895, 687, 2719, 7805, 1939, 16615}}, {1972, 15, 901, {1, 3, 7, 11, 11, 63, 35, 131, 269, 419, 1531, 535, 87, 1667, 2889}}, {1973, 15, 902, {1, 3, 7, 15, 31, 51, 13, 75, 411, 943, 1753, 797, 5287, 10133, 19235}}, {1974, 15, 906, {1, 3, 5, 15, 7, 37, 113, 169, 103, 305, 1059, 1769, 4801, 1743, 25455}}, {1975, 15, 916, {1, 1, 3, 5, 1, 33, 53, 203, 247, 697, 851, 3927, 6737, 5455, 1709}}, {1976, 15, 920, {1, 1, 7, 9, 7, 5, 9, 201, 321, 613, 1567, 859, 3543, 2357, 11377}}, {1977, 15, 949, {1, 1, 3, 11, 29, 11, 105, 217, 99, 971, 19, 3007, 6573, 3381, 22739}}, {1978, 15, 962, {1, 3, 5, 1, 1, 11, 83, 215, 15, 217, 731, 873, 1275, 11457, 26937}}, {1979, 15, 964, {1, 1, 7, 15, 19, 29, 11, 235, 193, 713, 629, 1205, 6655, 1669, 3465}}, {1980, 15, 967, {1, 1, 7, 1, 13, 49, 89, 73, 39, 45, 301, 3723, 4603, 12853, 13695}}, {1981, 15, 981, {1, 3, 3, 11, 27, 1, 51, 223, 495, 153, 835, 3565, 465, 9497, 8303}}, {1982, 15, 982, {1, 1, 1, 5, 11, 25, 7, 99, 141, 247, 1335, 2307, 4639, 375, 16841}}, {1983, 15, 985, {1, 1, 7, 11, 21, 11, 81, 123, 485, 363, 217, 2165, 4819, 11045, 9853}}, {1984, 15, 991, {1, 3, 5, 7, 15, 43, 17, 19, 377, 601, 849, 1157, 7821, 5623, 29901}}, {1985, 15, 1007, {1, 3, 3, 13, 15, 29, 93, 87, 445, 565, 561, 4025, 79, 12369, 30383}}, {1986, 15, 1016, {1, 1, 3, 11, 11, 13, 31, 239, 485, 417, 1785, 1843, 2807, 1539, 15727}}, {1987, 15, 1024, {1, 3, 1, 9, 17, 17, 7, 109, 239, 243, 53, 575, 77, 4887, 8023}}, {1988, 15, 1051, {1, 3, 3, 7, 29, 57, 85, 161, 155, 667, 243, 581, 6307, 1947, 7165}}, {1989, 15, 1060, {1, 3, 5, 13, 11, 37, 83, 231, 255, 899, 1795, 3049, 7169, 11451, 31227}}, {1990, 15, 1070, {1, 1, 3, 5, 29, 7, 19, 143, 53, 191, 1525, 2685, 1377, 6229, 25141}}, {1991, 15, 1072, {1, 3, 1, 15, 1, 31, 77, 207, 445, 217, 337, 1355, 7057, 6147, 24061}}, {1992, 15, 1084, {1, 1, 7, 5, 3, 19, 39, 25, 23, 49, 85, 781, 6347, 1137, 30013}}, {1993, 15, 1089, {1, 1, 7, 13, 25, 57, 51, 111, 201, 73, 983, 931, 1085, 8227, 21791}}, {1994, 15, 1095, {1, 1, 7, 13, 31, 41, 15, 223, 371, 117, 103, 589, 7819, 7991, 19903}}, {1995, 15, 1114, {1, 1, 1, 3, 29, 15, 119, 229, 163, 825, 1299, 339, 5861, 13927, 9923}}, {1996, 15, 1123, {1, 3, 1, 3, 7, 63, 31, 69, 181, 445, 1501, 663, 4915, 7387, 22065}}, {1997, 15, 1132, {1, 1, 5, 15, 25, 19, 69, 147, 233, 713, 1697, 1685, 2705, 6261, 1805}}, {1998, 15, 1154, {1, 3, 3, 11, 5, 21, 1, 235, 481, 349, 749, 853, 7893, 10075, 26307}}, {1999, 15, 1156, {1, 3, 5, 11, 7, 61, 115, 133, 227, 69, 1741, 4011, 1911, 4579, 7941}}, {2000, 15, 1163, {1, 3, 7, 13, 15, 45, 51, 127, 467, 353, 1947, 2129, 2969, 3185, 24177}}, {2001, 15, 1171, {1, 1, 5, 11, 25, 19, 29, 105, 483, 795, 1015, 975, 7037, 11439, 7217}}, {2002, 15, 1202, {1, 3, 7, 9, 17, 61, 121, 143, 133, 281, 1101, 3033, 1081, 5371, 13073}}, {2003, 15, 1228, {1, 1, 7, 9, 11, 19, 7, 61, 147, 1011, 1315, 2641, 4065, 13461, 19589}}, {2004, 15, 1239, {1, 3, 5, 3, 7, 1, 111, 123, 51, 345, 1033, 3863, 5135, 4907, 12509}}, {2005, 15, 1255, {1, 3, 3, 7, 3, 57, 45, 207, 487, 751, 145, 3037, 1467, 8917, 20379}}, {2006, 15, 1256, {1, 3, 3, 11, 15, 43, 123, 195, 15, 233, 1997, 2095, 2755, 16347, 3809}}, {2007, 15, 1262, {1, 1, 7, 3, 21, 5, 17, 253, 153, 25, 563, 139, 2611, 12733, 17505}}, {2008, 15, 1270, {1, 3, 1, 7, 27, 43, 33, 33, 489, 441, 1845, 3507, 5089, 1173, 14689}}, {2009, 15, 1279, {1, 1, 3, 7, 19, 43, 73, 165, 159, 873, 625, 1621, 5327, 8421, 14479}}, {2010, 15, 1308, {1, 3, 5, 7, 31, 37, 35, 195, 373, 257, 1791, 2679, 1517, 1649, 13101}}, {2011, 15, 1322, {1, 3, 1, 15, 11, 25, 127, 105, 65, 169, 931, 2445, 2953, 11405, 12267}}, {2012, 15, 1329, {1, 3, 7, 9, 25, 49, 1, 25, 273, 405, 1401, 265, 1449, 8641, 31469}}, {2014, 15, 1330, {1, 3, 3, 9, 23, 3, 5, 99, 439, 521, 317, 1397, 6933, 14937, 15165}}, {2014, 15, 1336, {1, 1, 1, 5, 1, 25, 9, 137, 173, 1003, 625, 2783, 4179, 6203, 29619}}, {2015, 15, 1341, {1, 3, 7, 1, 7, 31, 49, 251, 269, 107, 659, 1091, 3833, 2803, 11677}}, {2016, 15, 1347, {1, 1, 7, 5, 1, 25, 79, 255, 335, 585, 457, 2331, 3371, 12899, 8727}}, {2017, 15, 1349, {1, 1, 1, 9, 21, 37, 35, 115, 197, 587, 81, 2641, 3343, 10733, 17601}}, {2018, 15, 1359, {1, 1, 5, 1, 21, 9, 39, 95, 47, 289, 355, 183, 5063, 7409, 11539}}, {2019, 15, 1367, {1, 3, 1, 3, 23, 23, 11, 165, 65, 51, 597, 1657, 4625, 6489, 21539}}, {2020, 15, 1368, {1, 1, 5, 1, 27, 25, 83, 201, 445, 659, 703, 2129, 5537, 8669, 10197}}, {2021, 15, 1390, {1, 1, 7, 11, 29, 17, 27, 205, 321, 117, 1519, 3543, 1025, 9761, 3193}}, {2022, 15, 1413, {1, 3, 1, 13, 7, 17, 109, 3, 243, 495, 1541, 2153, 3391, 10359, 31065}}, {2023, 15, 1414, {1, 1, 7, 7, 19, 35, 79, 229, 413, 967, 1917, 1363, 5967, 8581, 6219}}, {2024, 15, 1437, {1, 3, 5, 7, 9, 25, 23, 187, 445, 879, 773, 3335, 7989, 16287, 20037}}, {2025, 15, 1441, {1, 3, 3, 15, 3, 1, 43, 99, 189, 567, 49, 3215, 3375, 1523, 7707}}, {2026, 15, 1462, {1, 3, 5, 5, 19, 37, 109, 173, 301, 35, 1231, 1891, 7891, 4673, 8549}}, {2027, 15, 1465, {1, 3, 3, 3, 9, 25, 115, 35, 63, 773, 289, 3361, 7127, 3485, 23359}}, {2028, 15, 1480, {1, 3, 5, 13, 21, 23, 113, 187, 59, 103, 1339, 3811, 3527, 1267, 26137}}, {2029, 15, 1486, {1, 1, 3, 15, 1, 61, 33, 173, 439, 607, 613, 3923, 2389, 3019, 30907}}, {2030, 15, 1504, {1, 3, 7, 15, 11, 55, 35, 51, 387, 585, 1919, 753, 6919, 10933, 11737}}, {2031, 15, 1509, {1, 3, 5, 15, 13, 9, 71, 125, 385, 679, 1887, 1205, 2873, 2691, 15301}}, {2032, 15, 1514, {1, 1, 1, 9, 15, 31, 89, 57, 149, 275, 261, 1777, 4015, 1333, 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7, 55, 49, 193, 271, 821, 103, 2551, 4089, 7225, 17055, 37139, 114215}}, {10117, 17, 37256, {1, 1, 3, 15, 13, 21, 109, 75, 159, 711, 645, 3363, 2595, 6665, 411, 21815, 121545}}, {10118, 17, 37264, {1, 3, 1, 3, 11, 31, 31, 175, 277, 537, 2035, 2649, 4629, 4765, 17291, 58759, 10223}}, {10119, 17, 37267, {1, 1, 7, 3, 9, 21, 57, 181, 285, 667, 109, 3247, 6881, 3713, 3667, 33743, 105161}}, {10120, 17, 37273, {1, 3, 5, 5, 1, 63, 51, 69, 293, 519, 1297, 3073, 7659, 829, 25307, 2187, 32613}}, {10121, 17, 37295, {1, 1, 5, 9, 11, 57, 29, 193, 427, 709, 1429, 1185, 4341, 5917, 2441, 53145, 32039}}, {10122, 17, 37315, {1, 1, 1, 7, 29, 55, 11, 71, 283, 223, 1999, 2597, 5887, 5097, 29055, 21741, 65855}}, {10123, 17, 37330, {1, 3, 3, 7, 13, 31, 101, 211, 323, 85, 961, 2833, 4357, 1745, 14945, 7077, 104591}}, {10124, 17, 37336, {1, 1, 3, 11, 17, 39, 125, 27, 327, 281, 87, 2341, 433, 15277, 20541, 44881, 107773}}, {10125, 17, 37339, {1, 3, 1, 15, 31, 7, 91, 63, 349, 103, 1101, 1049, 6527, 15471, 9253, 58841, 95553}}, {10126, 17, 37342, {1, 3, 1, 11, 9, 33, 15, 215, 141, 317, 1405, 1811, 7617, 3311, 24845, 7629, 445}}, {10127, 17, 37357, {1, 3, 3, 3, 13, 27, 27, 123, 7, 101, 1509, 2789, 3833, 16205, 24905, 29453, 106435}}, {10128, 17, 37365, {1, 3, 1, 13, 5, 51, 47, 87, 483, 791, 921, 4079, 6607, 14077, 1297, 41961, 86579}}, {10129, 17, 37372, {1, 3, 7, 3, 9, 23, 83, 227, 321, 397, 1483, 1857, 7191, 9211, 4511, 7547, 82415}}, {10130, 17, 37381, {1, 1, 7, 13, 15, 43, 47, 135, 211, 497, 1827, 2493, 2475, 2011, 25013, 44627, 13675}}, {10131, 17, 37399, {1, 3, 3, 11, 23, 47, 73, 199, 467, 111, 27, 209, 6941, 8929, 6413, 3329, 97825}}, {10132, 17, 37416, {1, 1, 1, 13, 31, 49, 67, 199, 229, 935, 791, 141, 2829, 11861, 9791, 15445, 17437}}, {10133, 17, 37429, {1, 1, 5, 7, 17, 25, 47, 23, 313, 59, 371, 3865, 5767, 6461, 2973, 10165, 48247}}, {10134, 17, 37436, {1, 3, 7, 3, 25, 47, 37, 51, 371, 101, 249, 91, 3985, 10239, 10423, 33433, 109067}}, {10135, 17, 37442, {1, 3, 1, 3, 27, 33, 67, 75, 167, 961, 493, 1875, 4005, 13019, 27085, 17967, 107771}}, {10136, 17, 37451, {1, 1, 1, 3, 17, 23, 37, 179, 459, 907, 55, 2049, 5273, 4059, 30429, 10273, 70159}}, {10137, 17, 37453, {1, 1, 5, 9, 13, 33, 71, 143, 325, 767, 1871, 3989, 7991, 3555, 28937, 48259, 60243}}, {10138, 17, 37475, {1, 1, 1, 9, 25, 27, 111, 43, 265, 11, 1443, 3161, 3473, 1451, 3789, 42431, 117069}}, {10139, 17, 37482, {1, 1, 1, 1, 29, 1, 121, 25, 501, 781, 1429, 1495, 6125, 11293, 30063, 1713, 7071}}, {10140, 17, 37489, {1, 1, 3, 15, 23, 27, 15, 145, 255, 207, 1977, 567, 469, 11589, 1535, 61637, 89569}}, {10141, 17, 37490, {1, 3, 5, 5, 13, 45, 113, 215, 65, 531, 335, 1275, 53, 447, 24887, 29829, 33391}}, {10142, 17, 37523, {1, 1, 1, 3, 5, 55, 89, 97, 197, 467, 95, 2603, 7789, 13289, 29911, 21935, 122947}}, {10143, 17, 37525, {1, 1, 3, 11, 21, 3, 61, 9, 363, 417, 1027, 2457, 3169, 11207, 27551, 41991, 71381}}, {10144, 17, 37530, {1, 3, 5, 11, 19, 57, 107, 29, 249, 93, 1235, 1239, 6491, 14695, 2407, 41513, 25779}}, {10145, 17, 37535, {1, 1, 3, 13, 5, 43, 3, 247, 309, 553, 1349, 2693, 7609, 10099, 13021, 32371, 27705}}, {10146, 17, 37539, {1, 1, 3, 11, 7, 3, 37, 209, 153, 945, 459, 3281, 6749, 12267, 17103, 58285, 115593}}, {10147, 17, 37548, {1, 3, 1, 3, 19, 19, 113, 23, 363, 147, 203, 1673, 4005, 4983, 31463, 12695, 95089}}, {10148, 17, 37559, {1, 3, 5, 9, 3, 31, 77, 129, 217, 395, 1701, 15, 8181, 2327, 12441, 52889, 114339}}, {10149, 17, 37560, {1, 1, 1, 15, 5, 7, 81, 191, 45, 45, 903, 2561, 1303, 13435, 321, 41897, 79013}}, {10150, 17, 37566, {1, 3, 3, 13, 19, 33, 11, 67, 9, 649, 217, 2181, 2237, 2851, 7423, 37003, 119205}}, {10151, 17, 37597, {1, 3, 7, 11, 29, 5, 87, 117, 487, 693, 155, 3653, 1497, 10249, 31567, 5987, 59435}}, {10152, 17, 37601, {1, 3, 7, 5, 11, 5, 77, 251, 399, 257, 1429, 3487, 8097, 1919, 11635, 3833, 43577}}, {10153, 17, 37602, {1, 1, 7, 11, 21, 63, 83, 17, 83, 807, 1849, 639, 7453, 15427, 2617, 21403, 4131}}, {10154, 17, 37604, {1, 1, 7, 15, 19, 1, 43, 245, 89, 271, 635, 227, 5977, 6985, 3239, 44639, 50959}}, {10155, 17, 37616, {1, 3, 7, 1, 19, 25, 35, 41, 455, 919, 101, 1953, 6119, 15299, 16315, 58857, 107557}}, {10156, 17, 37622, {1, 1, 5, 5, 3, 27, 123, 81, 355, 327, 1645, 1439, 3497, 3133, 17, 7225, 83255}}, {10157, 17, 37658, {1, 1, 1, 15, 29, 31, 61, 15, 157, 161, 1751, 2687, 3539, 5695, 149, 8841, 23405}}, {10158, 17, 37660, {1, 1, 1, 15, 1, 27, 79, 231, 157, 275, 1687, 3083, 4547, 9929, 6181, 32653, 30727}}, {10159, 17, 37667, {1, 1, 1, 1, 29, 51, 95, 133, 311, 675, 1829, 2089, 7681, 13119, 32157, 10651, 9023}}, {10160, 17, 37684, {1, 3, 5, 11, 7, 11, 41, 137, 147, 623, 81, 253, 3159, 4501, 22465, 41047, 14253}}, {10161, 17, 37693, {1, 1, 5, 15, 9, 29, 35, 63, 265, 691, 1371, 4061, 6327, 10671, 9303, 58831, 122423}}, {10162, 17, 37694, {1, 3, 3, 13, 17, 43, 9, 173, 435, 805, 1679, 3261, 6681, 13295, 23511, 4575, 100573}}, {10163, 17, 37696, {1, 1, 3, 15, 7, 11, 93, 227, 285, 795, 1089, 927, 2187, 927, 4283, 29241, 75241}}, {10164, 17, 37706, {1, 1, 1, 7, 13, 7, 71, 167, 239, 411, 235, 1543, 5259, 9749, 4257, 30517, 18167}}, {10165, 17, 37711, {1, 1, 7, 7, 29, 37, 67, 245, 151, 627, 1245, 2967, 7821, 1113, 3243, 59403, 80303}}, {10166, 17, 37730, {1, 1, 5, 13, 31, 15, 9, 49, 81, 257, 31, 227, 201, 2127, 30581, 38487, 96959}}, {10167, 17, 37735, {1, 1, 5, 5, 21, 39, 61, 155, 47, 235, 355, 3397, 2973, 1029, 23497, 21007, 35183}}, {10168, 17, 37742, {1, 1, 3, 5, 7, 27, 87, 45, 89, 211, 519, 2621, 6299, 2049, 21225, 4975, 8799}}, {10169, 17, 37744, {1, 3, 5, 11, 7, 51, 19, 33, 153, 925, 1067, 3789, 7463, 8403, 1495, 37549, 20661}}, {10170, 17, 37759, {1, 1, 5, 1, 21, 53, 97, 147, 435, 329, 1635, 3069, 3353, 3969, 15555, 7171, 58141}}, {10171, 17, 37777, {1, 1, 1, 5, 31, 29, 103, 87, 89, 673, 1505, 2921, 3019, 3081, 7723, 11105, 7477}}, {10172, 17, 37783, {1, 1, 7, 5, 17, 15, 111, 15, 59, 851, 1351, 2365, 2427, 5035, 22341, 38511, 61813}}, {10173, 17, 37784, {1, 3, 5, 9, 21, 15, 35, 11, 149, 991, 981, 3855, 2783, 10405, 21113, 64173, 75199}}, {10174, 17, 37793, {1, 3, 5, 7, 19, 25, 99, 11, 101, 71, 1913, 1017, 4241, 15635, 15571, 33541, 79103}}, {10175, 17, 37800, {1, 3, 7, 9, 13, 19, 67, 75, 57, 257, 1623, 3641, 1745, 12747, 7171, 20861, 106387}}, {10176, 17, 37818, {1, 3, 1, 3, 9, 43, 29, 125, 453, 525, 1789, 2281, 1037, 14799, 27183, 7235, 97467}}, {10177, 17, 37823, {1, 3, 3, 15, 25, 19, 115, 73, 163, 557, 1365, 1205, 7845, 2977, 6293, 4039, 100505}}, {10178, 17, 37825, {1, 3, 7, 15, 11, 43, 109, 181, 153, 809, 25, 773, 3265, 6919, 23835, 63627, 79707}}, {10179, 17, 37828, {1, 3, 5, 13, 13, 9, 37, 209, 117, 49, 973, 2547, 2035, 7595, 15029, 9035, 83281}}, {10180, 17, 37832, {1, 3, 7, 1, 1, 53, 77, 213, 137, 321, 2031, 3373, 4457, 15395, 3301, 11631, 30925}}, {10181, 17, 37849, {1, 3, 5, 9, 21, 1, 39, 227, 1, 395, 1191, 1029, 6467, 11219, 32063, 1347, 98889}}, {10182, 17, 37856, {1, 3, 5, 15, 21, 21, 49, 169, 289, 785, 151, 2309, 7475, 4065, 17553, 35213, 63947}}, {10183, 17, 37861, {1, 1, 7, 13, 27, 1, 93, 245, 389, 211, 285, 1273, 6445, 4293, 53, 22689, 24989}}, {10184, 17, 37862, {1, 3, 5, 13, 27, 27, 37, 217, 225, 271, 9, 2547, 3381, 1599, 459, 19337, 125349}}, {10185, 17, 37886, {1, 3, 3, 5, 29, 45, 93, 239, 403, 985, 901, 3501, 1889, 15647, 25031, 6073, 14101}}, {10186, 17, 37893, {1, 3, 1, 9, 21, 5, 77, 171, 197, 677, 1571, 3925, 4917, 14415, 20147, 39871, 125939}}, {10187, 17, 37915, {1, 1, 5, 3, 3, 17, 19, 47, 499, 397, 667, 3373, 1771, 4453, 9519, 48939, 121915}}, {10188, 17, 37922, {1, 3, 3, 5, 29, 25, 121, 133, 367, 281, 131, 1115, 6359, 9621, 31137, 58021, 27117}}, {10189, 17, 37936, {1, 1, 3, 5, 23, 43, 45, 41, 261, 681, 1177, 2007, 5441, 1507, 11579, 54001, 69625}}, {10190, 17, 37939, {1, 3, 1, 3, 27, 61, 85, 167, 275, 285, 1, 919, 6439, 3331, 9483, 46613, 89019}}, {10191, 17, 37945, {1, 1, 7, 9, 25, 33, 37, 33, 211, 221, 273, 2257, 6565, 15801, 4911, 1781, 60147}}, {10192, 17, 37956, {1, 3, 5, 7, 7, 17, 81, 215, 511, 565, 327, 3327, 1439, 1573, 8959, 30037, 95635}}, {10193, 17, 37960, {1, 3, 5, 13, 23, 31, 75, 93, 421, 439, 2033, 2677, 593, 2729, 17641, 61789, 41253}}, {10194, 17, 37971, {1, 1, 3, 11, 21, 17, 45, 63, 77, 497, 439, 4077, 4047, 273, 3233, 54695, 22014}}, {10195, 17, 37980, {1, 3, 1, 7, 5, 17, 125, 29, 365, 887, 1915, 3455, 391, 9435, 14723, 34807, 52475}}, {10196, 17, 38002, {1, 1, 7, 11, 29, 49, 71, 165, 491, 721, 627, 3777, 7295, 2549, 7521, 35637, 14447}}, {10197, 17, 38007, {1, 3, 7, 13, 3, 3, 121, 193, 273, 241, 889, 13, 3445, 3313, 20381, 39921, 16609}}, {10198, 17, 38018, {1, 3, 7, 13, 5, 49, 61, 123, 443, 769, 1669, 2741, 6881, 5965, 9365, 43051, 2979}}, {10199, 17, 38020, {1, 1, 1, 7, 7, 25, 41, 179, 419, 225, 1827, 613, 4711, 1671, 14459, 33951, 56751}}, {10200, 17, 38038, {1, 3, 5, 7, 9, 61, 35, 205, 243, 49, 803, 2653, 4101, 4435, 29697, 45441, 124841}} // Extending this table? // Ensure that the max_m defined in sobol_primitives.h is sufficient for all the m values };