ATen/native/SobolEngineOpsUtils.cpp

/// This file contains tensor-agnostic SoboleEngine constants
#define TORCH_ASSERT_ONLY_METHOD_OPERATORS
#include <ATen/native/SobolEngineOpsUtils.h>

/*
The direction numbers in this file  were generated using the
python script below (thius this assumes that the file
https://web.maths.unsw.edu.au/~fkuo/sobol/new-joe-kuo-6.21201
is present in the working directory). For additional details see [1].

[1] S. Joe and F. Y. Kuo. Remark on algorithm 659: Implementing
    sobol’s quasirandom sequence generator.
    ACM Trans. Math. Softw., 29(1):49–57, Mar. 2003.


    import pandas as pd
    import numpy as np

    # read in file content
    with open("./new-joe-kuo-6.21201", "r") as f:
        lines = f.readlines()
    rows = []

    # parse data from file line by line
    for l in lines[1:]:
        nums = [int(n) for n in l.replace(" \n", "").split()]
        d, s, a = nums[:3]
        vs = {f"v{i}": int(v) for i,v in enumerate(nums[3:])}
        rows.append({"d": d, "s": s, "a": a, **vs})

    # read in as dataframe, explicitly use zero values
    df = pd.DataFrame(rows).fillna(0).astype(int)

    # peform conversion according to Section 2.1 of [1]
    df["poly"] = 2 * df["a"] + 2 ** df["s"] + 1

    # ensure columns are properly ordered
    vs = df[[f"v{i}" for i in range(18)]].values

    # add the degenerate d=1 column (not included in the data file)
    initsobolstate = np.vstack([vs[0][np.newaxis, :], vs])
    poly = np.concatenate([[1], df["poly"].values])
*/

namespace at::native::sobol_utils {

/// All definitions below this point are data. These are constant, and should
/// not be modified without notice
// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,modernize-avoid-c-arrays)
const int64_t poly[21201] = {
    1,
    3,
    7,
    11,
    13,
    19,
    25,
    37,
    41,
    47,
    55,
    59,
    61,
    67,
    91,
    97,
    103,
    109,
    115,
    131,
    137,
    143,
    145,
    157,
    167,
    171,
    185,
    191,
    193,
    203,
    211,
    213,
    229,
    239,
    241,
    247,
    253,
    285,
    299,
    301,
    333,
    351,
    355,
    357,
    361,
    369,
    391,
    397,
    425,
    451,
    463,
    487,
    501,
    529,
    539,
    545,
    557,
    563,
    601,
    607,
    617,
    623,
    631,
    637,
    647,
    661,
    675,
    677,
    687,
    695,
    701,
    719,
    721,
    731,
    757,
    761,
    787,
    789,
    799,
    803,
    817,
    827,
    847,
    859,
    865,
    875,
    877,
    883,
    895,
    901,
    911,
    949,
    953,
    967,
    971,
    973,
    981,
    985,
    995,
    1001,
    1019,
    1033,
    1051,
    1063,
    1069,
    1125,
    1135,
    1153,
    1163,
    1221,
    1239,
    1255,
    1267,
    1279,
    1293,
    1305,
    1315,
    1329,
    1341,
    1347,
    1367,
    1387,
    1413,
    1423,
    1431,
    1441,
    1479,
    1509,
    1527,
    1531,
    1555,
    1557,
    1573,
    1591,
    1603,
    1615,
    1627,
    1657,
    1663,
    1673,
    1717,
    1729,
    1747,
    1759,
    1789,
    1815,
    1821,
    1825,
    1849,
    1863,
    1869,
    1877,
    1881,
    1891,
    1917,
    1933,
    1939,
    1969,
    2011,
    2035,
    2041,
    2053,
    2071,
    2091,
    2093,
    2119,
    2147,
    2149,
    2161,
    2171,
    2189,
    2197,
    2207,
    2217,
    2225,
    2255,
    2257,
    2273,
    2279,
    2283,
    2293,
    2317,
    2323,
    2341,
    2345,
    2363,
    2365,
    2373,
    2377,
    2385,
    2395,
    2419,
    2421,
    2431,
    2435,
    2447,
    2475,
    2477,
    2489,
    2503,
    2521,
    2533,
    2551,
    2561,
    2567,
    2579,
    2581,
    2601,
    2633,
    2657,
    2669,
    2681,
    2687,
    2693,
    2705,
    2717,
    2727,
    2731,
    2739,
    2741,
    2773,
    2783,
    2793,
    2799,
    2801,
    2811,
    2819,
    2825,
    2833,
    2867,
    2879,
    2881,
    2891,
    2905,
    2911,
    2917,
    2927,
    2941,
    2951,
    2955,
    2963,
    2965,
    2991,
    2999,
    3005,
    3017,
    3035,
    3037,
    3047,
    3053,
    3083,
    3085,
    3097,
    3103,
    3159,
    3169,
    3179,
    3187,
    3205,
    3209,
    3223,
    3227,
    3229,
    3251,
    3263,
    3271,
    3277,
    3283,
    3285,
    3299,
    3305,
    3319,
    3331,
    3343,
    3357,
    3367,
    3373,
    3393,
    3399,
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    3417,
    3427,
    3439,
    3441,
    3475,
    3487,
    3497,
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    3517,
    3529,
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    3547,
    3553,
    3559,
    3573,
    3589,
    3613,
    3617,
    3623,
    3627,
    3635,
    3641,
    3655,
    3659,
    3669,
    3679,
    3697,
    3707,
    3709,
    3713,
    3731,
    3743,
    3747,
    3771,
    3791,
    3805,
    3827,
    3833,
    3851,
    3865,
    3889,
    3895,
    3933,
    3947,
    3949,
    3957,
    3971,
    3985,
    3991,
    3995,
    4007,
    4013,
    4021,
    4045,
    4051,
    4069,
    4073,
    4179,
    4201,
    4219,
    4221,
    4249,
    4305,
    4331,
    4359,
    4383,
    4387,
    4411,
    4431,
    4439,
    4449,
    4459,
    4485,
    4531,
    4569,
    4575,
    4621,
    4663,
    4669,
    4711,
    4723,
    4735,
    4793,
    4801,
    4811,
    4879,
    4893,
    4897,
    4921,
    4927,
    4941,
    4977,
    5017,
    5027,
    5033,
    5127,
    5169,
    5175,
    5199,
    5213,
    5223,
    5237,
    5287,
    5293,
    5331,
    5391,
    5405,
    5453,
    5523,
    5573,
    5591,
    5597,
    5611,
    5641,
    5703,
    5717,
    5721,
    5797,
    5821,
    5909,
    5913,
    5955,
    5957,
    6005,
    6025,
    6061,
    6067,
    6079,
    6081,
    6231,
    6237,
    6289,
    6295,
    6329,
    6383,
    6427,
    6453,
    6465,
    6501,
    6523,
    6539,
    6577,
    6589,
    6601,
    6607,
    6631,
    6683,
    6699,
    6707,
    6761,
    6795,
    6865,
    6881,
    6901,
    6923,
    6931,
    6943,
    6999,
    7057,
    7079,
    7103,
    7105,
    7123,
    7173,
    7185,
    7191,
    7207,
    7245,
    7303,
    7327,
    7333,
    7355,
    7365,
    7369,
    7375,
    7411,
    7431,
    7459,
    7491,
    7505,
    7515,
    7541,
    7557,
    7561,
    7701,
    7705,
    7727,
    7749,
    7761,
    7783,
    7795,
    7823,
    7907,
    7953,
    7963,
    7975,
    8049,
    8089,
    8123,
    8125,
    8137,
    8219,
    8231,
    8245,
    8275,
    8293,
    8303,
    8331,
    8333,
    8351,
    8357,
    8367,
    8379,
    8381,
    8387,
    8393,
    8417,
    8435,
    8461,
    8469,
    8489,
    8495,
    8507,
    8515,
    8551,
    8555,
    8569,
    8585,
    8599,
    8605,
    8639,
    8641,
    8647,
    8653,
    8671,
    8675,
    8689,
    8699,
    8729,
    8741,
    8759,
    8765,
    8771,
    8795,
    8797,
    8825,
    8831,
    8841,
    8855,
    8859,
    8883,
    8895,
    8909,
    8943,
    8951,
    8955,
    8965,
    8999,
    9003,
    9031,
    9045,
    9049,
    9071,
    9073,
    9085,
    9095,
    9101,
    9109,
    9123,
    9129,
    9137,
    9143,
    9147,
    9185,
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    9209,
    9227,
    9235,
    9247,
    9253,
    9257,
    9277,
    9297,
    9303,
    9313,
    9325,
    9343,
    9347,
    9371,
    9373,
    9397,
    9407,
    9409,
    9415,
    9419,
    9443,
    9481,
    9495,
    9501,
    9505,
    9517,
    9529,
    9555,
    9557,
    9571,
    9585,
    9591,
    9607,
    9611,
    9621,
    9625,
    9631,
    9647,
    9661,
    9669,
    9679,
    9687,
    9707,
    9731,
    9733,
    9745,
    9773,
    9791,
    9803,
    9811,
    9817,
    9833,
    9847,
    9851,
    9863,
    9875,
    9881,
    9905,
    9911,
    9917,
    9923,
    9963,
    9973,
    10003,
    10025,
    10043,
    10063,
    10071,
    10077,
    10091,
    10099,
    10105,
    10115,
    10129,
    10145,
    10169,
    10183,
    10187,
    10207,
    10223,
    10225,
    10247,
    10265,
    10271,
    10275,
    10289,
    10299,
    10301,
    10309,
    10343,
    10357,
    10373,
    10411,
    10413,
    10431,
    10445,
    10453,
    10463,
    10467,
    10473,
    10491,
    10505,
    10511,
    10513,
    10523,
    10539,
    10549,
    10559,
    10561,
    10571,
    10581,
    10615,
    10621,
    10625,
    10643,
    10655,
    10671,
    10679,
    10685,
    10691,
    10711,
    10739,
    10741,
    10755,
    10767,
    10781,
    10785,
    10803,
    10805,
    10829,
    10857,
    10863,
    10865,
    10875,
    10877,
    10917,
    10921,
    10929,
    10949,
    10967,
    10971,
    10987,
    10995,
    11009,
    11029,
    11043,
    11045,
    11055,
    11063,
    11075,
    11081,
    11117,
    11135,
    11141,
    11159,
    11163,
    11181,
    11187,
    11225,
    11237,
    11261,
    11279,
    11297,
    11307,
    11309,
    11327,
    11329,
    11341,
    11377,
    11403,
    11405,
    11413,
    11427,
    11439,
    11453,
    11461,
    11473,
    11479,
    11489,
    11495,
    11499,
    11533,
    11545,
    11561,
    11567,
    11575,
    11579,
    11589,
    11611,
    11623,
    11637,
    11657,
    11663,
    11687,
    11691,
    11701,
    11747,
    11761,
    11773,
    11783,
    11795,
    11797,
    11817,
    11849,
    11855,
    11867,
    11869,
    11873,
    11883,
    11919,
    11921,
    11927,
    11933,
    11947,
    11955,
    11961,
    11999,
    12027,
    12029,
    12037,
    12041,
    12049,
    12055,
    12095,
    12097,
    12107,
    12109,
    12121,
    12127,
    12133,
    12137,
    12181,
    12197,
    12207,
    12209,
    12239,
    12253,
    12263,
    12269,
    12277,
    12287,
    12295,
    12309,
    12313,
    12335,
    12361,
    12367,
    12391,
    12409,
    12415,
    12433,
    12449,
    12469,
    12479,
    12481,
    12499,
    12505,
    12517,
    12527,
    12549,
    12559,
    12597,
    12615,
    12621,
    12639,
    12643,
    12657,
    12667,
    12707,
    12713,
    12727,
    12741,
    12745,
    12763,
    12769,
    12779,
    12781,
    12787,
    12799,
    12809,
    12815,
    12829,
    12839,
    12857,
    12875,
    12883,
    12889,
    12901,
    12929,
    12947,
    12953,
    12959,
    12969,
    12983,
    12987,
    12995,
    13015,
    13019,
    13031,
    13063,
    13077,
    13103,
    13137,
    13149,
    13173,
    13207,
    13211,
    13227,
    13241,
    13249,
    13255,
    13269,
    13283,
    13285,
    13303,
    13307,
    13321,
    13339,
    13351,
    13377,
    13389,
    13407,
    13417,
    13431,
    13435,
    13447,
    13459,
    13465,
    13477,
    13501,
    13513,
    13531,
    13543,
    13561,
    13581,
    13599,
    13605,
    13617,
    13623,
    13637,
    13647,
    13661,
    13677,
    13683,
    13695,
    13725,
    13729,
    13753,
    13773,
    13781,
    13785,
    13795,
    13801,
    13807,
    13825,
    13835,
    13855,
    13861,
    13871,
    13883,
    13897,
    13905,
    13915,
    13939,
    13941,
    13969,
    13979,
    13981,
    13997,
    14027,
    14035,
    14037,
    14051,
    14063,
    14085,
    14095,
    14107,
    14113,
    14125,
    14137,
    14145,
    14151,
    14163,
    14193,
    14199,
    14219,
    14229,
    14233,
    14243,
    14277,
    14287,
    14289,
    14295,
    14301,
    14305,
    14323,
    14339,
    14341,
    14359,
    14365,
    14375,
    14387,
    14411,
    14425,
    14441,
    14449,
    14499,
    14513,
    14523,
    14537,
    14543,
    14561,
    14579,
    14585,
    14593,
    14599,
    14603,
    14611,
    14641,
    14671,
    14695,
    14701,
    14723,
    14725,
    14743,
    14753,
    14759,
    14765,
    14795,
    14797,
    14803,
    14831,
    14839,
    14845,
    14855,
    14889,
    14895,
    14909,
    14929,
    14941,
    14945,
    14951,
    14963,
    14965,
    14985,
    15033,
    15039,
    15053,
    15059,
    15061,
    15071,
    15077,
    15081,
    15099,
    15121,
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    15157,
    15167,
    15187,
    15193,
    15203,
    15205,
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    15217,
    15223,
    15243,
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    15269,
    15273,
    15287,
    15291,
    15313,
    15335,
    15347,
    15359,
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    15439,
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    15469,
    15491,
    15503,
    15517,
    15527,
    15531,
    15545,
    15559,
    15593,
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    15613,
    15619,
    15639,
    15643,
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    15661,
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    15669,
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    15721,
    15741,
    15745,
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    15825,
    15835,
    15847,
    15851,
    15865,
    15877,
    15881,
    15887,
    15899,
    15915,
    15935,
    15937,
    15955,
    15973,
    15977,
    16011,
    16035,
    16061,
    16069,
    16087,
    16093,
    16097,
    16121,
    16141,
    16153,
    16159,
    16165,
    16183,
    16189,
    16195,
    16197,
    16201,
    16209,
    16215,
    16225,
    16259,
    16265,
    16273,
    16299,
    16309,
    16355,
    16375,
    16381,
    16427,
    16441,
    16467,
    16479,
    16507,
    16553,
    16559,
    16571,
    16573,
    16591,
    16619,
    16627,
    16653,
    16659,
    16699,
    16707,
    16795,
    16797,
    16807,
    16813,
    16821,
    16853,
    16857,
    16881,
    16909,
    16983,
    16993,
    17023,
    17029,
    17053,
    17095,
    17099,
    17101,
    17123,
    17129,
    17135,
    17161,
    17185,
    17215,
    17277,
    17287,
    17301,
    17327,
    17353,
    17387,
    17389,
    17419,
    17475,
    17523,
    17619,
    17621,
    17631,
    17635,
    17659,
    17707,
    17721,
    17753,
    17775,
    17817,
    17823,
    17829,
    17847,
    17861,
    17879,
    17895,
    17907,
    17919,
    17935,
    17949,
    17959,
    17973,
    17991,
    18009,
    18019,
    18033,
    18043,
    18085,
    18117,
    18127,
    18139,
    18225,
    18255,
    18303,
    18343,
    18369,
    18405,
    18409,
    18415,
    18451,
    18457,
    18491,
    18499,
    18523,
    18529,
    18535,
    18559,
    18563,
    18659,
    18717,
    18733,
    18745,
    18793,
    18807,
    18823,
    18857,
    18895,
    18913,
    18997,
    19045,
    19067,
    19073,
    19079,
    19083,
    19107,
    19145,
    19165,
    19193,
    19255,
    19273,
    19291,
    19307,
    19309,
    19315,
    19321,
    19333,
    19351,
    19361,
    19371,
    19385,
    19403,
    19405,
    19413,
    19423,
    19441,
    19451,
    19465,
    19485,
    19519,
    19527,
    19531,
    19541,
    19581,
    19597,
    19621,
    19645,
    19653,
    19665,
    19671,
    19693,
    19743,
    19761,
    19781,
    19791,
    19793,
    19829,
    19855,
    19885,
    19891,
    19905,
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    490769,
    490781,
    490841,
    490899,
    490911,
    490917,
    491007,
    491041,
    491103,
    491119,
    491171,
    491229,
    491289,
    491313,
    491345,
    491355,
    491391,
    491401,
    491425,
    491445,
    491481,
    491487,
    491493,
    491545,
    491607,
    491641,
    491663,
    491677,
    491681,
    491713,
    491761,
    491771,
    491803,
    491805,
    491829,
    491895,
    491941,
    491951,
    491971,
    492001,
    492019,
    492061,
    492071,
    492145,
    492181,
    492191,
    492201,
    492229,
    492313,
    492337,
    492355,
    492379,
    492443,
    492455,
    492541,
    492587,
    492589,
    492595,
    492697,
    492733,
    492739,
    492787,
    492841,
    492873,
    492897,
    492915,
    492917,
    492945,
    492973,
    493075,
    493115,
    493129,
    493147,
    493183,
    493199,
    493207,
    493279,
    493289,
    493407,
    493441,
    493465,
    493489,
    493507,
    493521,
    493533,
    493543,
    493583,
    493597,
    493611,
    493737,
    493903,
    493905,
    493921,
    493961,
    493995,
    494029,
    494101,
    494117,
    494173,
    494183,
    494207,
    494241,
    494283,
    494327,
    494351,
    494359,
    494435,
    494449,
    494639,
    494723,
    494777,
    494833,
    494853,
    494881,
    494899,
    494911,
    494919,
    494961,
    495001,
    495035,
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    495109,
    495121,
    495131,
    495149,
    495181,
    495193,
    495199,
    495243,
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    495269,
    495281,
    495299,
    495325,
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    495397,
    495419,
    495439,
    495475,
    495493,
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    495573,
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    495633,
    495673,
    495693,
    495701,
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    495751,
    495757,
    495799,
    495823,
    495871,
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    495909,
    495919,
    495975,
    496023,
    496033,
    496051,
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    496149,
    496159,
    496175,
    496209,
    496215,
    496249,
    496319,
    496423,
    496459,
    496531,
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    496573,
    496585,
    496621,
    496641,
    496695,
    496731,
    496747,
    496783,
    496821,
    496839,
    496867,
    496905,
    496923,
    496941,
    497015,
    497061,
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    497141,
    497145,
    497203,
    497253,
    497257,
    497275,
    497305,
    497315,
    497329,
    497339,
    497377,
    497419,
    497433,
    497463,
    497551,
    497553,
    497599,
    497621,
    497685,
    497737,
    497743,
    497785,
    497809,
    497825,
    497831,
    497875,
    497881,
    497893,
    497917,
    498069,
    498079,
    498135,
    498145,
    498179,
    498219,
    498221,
    498247,
    498259,
    498289,
    498305,
    498341,
    498359,
    498363,
    498373,
    498391,
    498445,
    498463,
    498473,
    498491,
    498547,
    498569,
    498637,
    498659,
    498751,
    498765,
    498771,
    498793,
    498813,
    498817,
    498823,
    498851,
    498853,
    498925,
    498937,
    499017,
    499051,
    499077,
    499129,
    499157,
    499195,
    499259,
    499267,
    499317,
    499357,
    499399,
    499427,
    499453,
    499519,
    499521,
    499615,
    499619,
    499645,
    499691,
    499701,
    499717,
    499763,
    499811,
    499851,
    499853,
    499871,
    499907,
    499937,
    499979,
    499987,
    500023,
    500041,
    500065,
    500085,
    500111,
    500195,
    500197,
    500273,
    500283,
    500303,
    500315,
    500375,
    500475,
    500477,
    500531,
    500533,
    500543,
    500575,
    500581,
    500627,
    500699,
    500747,
    500757,
    500815,
    500833,
    500873,
    500891,
    500909,
    500965,
    500995,
    501063,
    501091,
    501117,
    501145,
    501161,
    501167,
    501179,
    501201,
    501211,
    501223,
    501229,
    501237,
    501277,
    501319,
    501325,
    501359,
    501373,
    501395,
    501411,
    501413,
    501431,
    501511,
    501553,
    501565,
    501613,
    501649,
    501665,
    501797,
    501989,
    502007,
    502099,
    502175,
    502185,
    502311,
    502317,
    502347,
    502355,
    502455,
    502521,
    502535,
    502577,
    502601,
    502621,
    502655,
    502779,
    502799,
    502883,
    502909,
    502953,
    502973,
    503009,
    503015,
    503053,
    503071,
    503087,
    503155,
    503201,
    503321,
    503377,
    503405,
    503433,
    503489,
    503499,
    503581,
    503595,
    503605,
    503657,
    503663,
    503675,
    503735,
    503787,
    503845,
    503881,
    503905,
    503915,
    503929,
    503939,
    503969,
    504013,
    504127,
    504153,
    504187,
    504189,
    504217,
    504227,
    504283,
    504301,
    504397,
    504415,
    504421,
    504469,
    504497,
    504517,
    504563,
    504569,
    504587,
    504595,
    504601,
    504623,
    504635,
    504673,
    504685,
    504743,
    504757,
    504775,
    504779,
    504787,
    504793,
    504805,
    504823,
    504837,
    504885,
    504889,
    504931,
    504937,
    504973,
    505029,
    505095,
    505143,
    505169,
    505181,
    505321,
    505339,
    505369,
    505403,
    505405,
    505413,
    505505,
    505595,
    505741,
    505775,
    505789,
    505819,
    505825,
    505883,
    505901,
    505939,
    505985,
    506003,
    506033,
    506143,
    506161,
    506257,
    506269,
    506279,
    506311,
    506335,
    506365,
    506381,
    506399,
    506523,
    506559,
    506597,
    506651,
    506747,
    506793,
    506819,
    506869,
    506881,
    506887,
    506901,
    506953,
    507031,
    507047,
    507059,
    507061,
    507103,
    507113,
    507187,
    507225,
    507235,
    507249,
    507265,
    507295,
    507301,
    507355,
    507467,
    507491,
    507589,
    507601,
    507623,
    507647,
    507669,
    507683,
    507689,
    507709,
    507741,
    507765,
    507769,
    507781,
    507803,
    507847,
    507859,
    507881,
    507931,
    507933,
    507949,
    507987,
    508063,
    508113,
    508147,
    508221,
    508297,
    508345,
    508359,
    508389,
    508423,
    508495,
    508525,
    508547,
    508583,
    508609,
    508655,
    508715,
    508801,
    508915,
    508939,
    508953,
    508983,
    509015,
    509019,
    509031,
    509145,
    509157,
    509167,
    509169,
    509181,
    509189,
    509235,
    509289,
    509319,
    509333,
    509359,
    509361,
    509405,
    509415,
    509463,
    509529,
    509535,
    509545,
    509605,
    509641,
    509647,
    509685,
    509731,
    509745,
    509751,
    509847,
    509863,
    509877,
    509881,
    509899,
    509913,
    509963,
    509965,
    509983,
    509999,
    510019,
    510045,
    510059,
    510103,
    510137,
    510225,
    510253,
    510271,
    510279,
    510321,
    510347,
    510453,
    510469,
    510479,
    510497,
    510535,
    510605,
    510679,
    510837,
    510923,
    510981,
    510985,
    511053,
    511125,
    511151,
    511183,
    511211,
    511233,
    511323,
    511377,
    511405,
    511417,
    511435,
    511449,
    511471,
    511479,
    511525,
    511655,
    511659,
    511783,
    511869,
    511873,
    511893,
    511909,
    511951,
    511975,
    512021,
    512035,
    512091,
    512117,
    512127,
    512167,
    512173,
    512309,
    512355,
    512471,
    512475,
    512555,
    512583,
    512623,
    512625,
    512659,
    512713,
    512749,
    512799,
    512817,
    512855,
    512871,
    512875,
    512889,
    512901,
    512911,
    512919,
    512925,
    512973,
    513015,
    513077,
    513107,
    513189,
    513207,
    513233,
    513273,
    513321,
    513349,
    513371,
    513387,
    513441,
    513447,
    513507,
    513583,
    513691,
    513693,
    513703,
    513717,
    513729,
    513789,
    513801,
    513807,
    513819,
    513905,
    513927,
    513989,
    514001,
    514007,
    514027,
    514041,
    514065,
    514091,
    514173,
    514177,
    514217,
    514231,
    514269,
    514297,
    514377,
    514395,
    514435,
    514449,
    514495,
    514521,
    514543,
    514555,
    514571,
    514585,
    514717,
    514733,
    514745,
    514789,
    514793,
    514831,
    514833,
    515005,
    515011,
    515041,
    515047,
    515059,
    515061,
    515071,
    515085,
    515113,
    515181,
    515187,
    515239,
    515257,
    515311,
    515313,
    515411,
    515491,
    515505,
    515517,
    515523,
    515549,
    515565,
    515589,
    515719,
    515723,
    515733,
    515747,
    515859,
    515927,
    515937,
    515949,
    515967,
    515983,
    516031,
    516039,
    516043,
    516051,
    516087,
    516097,
    516109,
    516163,
    516187,
    516199,
    516223,
    516227,
    516233,
    516263,
    516287,
    516295,
    516397,
    516403,
    516435,
    516453,
    516475,
    516487,
    516539,
    516541,
    516559,
    516597,
    516625,
    516653,
    516683,
    516755,
    516791,
    516829,
    516839,
    516871,
    516933,
    516997,
    517009,
    517025,
    517069,
    517081,
    517091,
    517117,
    517149,
    517165,
    517191,
    517231,
    517279,
    517285,
    517315,
    517321,
    517383,
    517387,
    517397,
    517401,
    517425,
    517469,
    517513,
    517519,
    517531,
    517537,
    517561,
    517567,
    517589,
    517609,
    517639,
    517679,
    517687,
    517725,
    517777,
    517793,
    517811,
    517883,
    517965,
    518001,
    518011,
    518071,
    518095,
    518177,
    518207,
    518263,
    518293,
    518359,
    518389,
    518459,
    518467,
    518545,
    518571,
    518603,
    518611,
    518627,
    518663,
    518735,
    518743,
    518771,
    518835,
    518869,
    518895,
    518897,
    518957,
    518965,
    518977,
    519031,
    519047,
    519075,
    519077,
    519113,
    519143,
    519149,
    519193,
    519217,
    519227,
    519229,
    519329,
    519341,
    519391,
    519409,
    519487,
    519571,
    519593,
    519607,
    519667,
    519679,
    519709,
    519731,
    519755,
    519785,
    519805,
    519829,
    519849,
    519863,
    519877,
    519895,
    519929,
    519937,
    519973,
    520015,
    520073,
    520091,
    520147,
    520159,
    520169,
    520187,
    520197,
    520255,
    520287,
    520331,
    520355,
    520393,
    520441,
    520447,
    520455,
    520467,
    520545,
    520593,
    520605,
    520619,
    520741,
    520745,
    520777,
    520835,
    520847,
    520849,
    520871,
    520931,
    520965,
    520975,
    521043,
    521099,
    521147,
    521181,
    521185,
    521235,
    521271,
    521333,
    521361,
    521377,
    521449,
    521463,
    521505,
    521529,
    521621,
    521673,
    521709,
    521731,
    521785,
    521793,
    521803,
    521841,
    521853,
    521867,
    521903,
    521917,
    521959,
    522043,
    522051,
    522105,
    522141,
    522207,
    522231,
    522259,
    522275,
    522319,
    522327,
    522337,
    522347,
    522367,
    522397,
    522419,
    522421,
    522443,
    522499,
    522505,
    522573,
    522601,
    522625,
    522679,
    522705,
    522733,
    522757,
    522795,
    522941,
    522949,
    522987,
    523021,
    523027,
    523095,
    523117,
    523151,
    523247,
    523293,
    523349,
    523369,
    523387,
    523411,
    523513,
    523521,
    523541,
    523545,
    523569,
    523623,
    523641,
    523693,
    523711,
    523749,
    523767,
    523817,
    523825,
    523857,
    523873,
    523891,
    523981,
    523999,
    524003,
    524061,
    524077,
    524085,
    524097,
    524157,
    524161,
    524185,
    524263,
};

// NOLINTNEXTLINE(cppcoreguidelines-avoid-c-arrays,modernize-avoid-c-arrays)
const int64_t initsobolstate[21201][18] = {
    {1, 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},
    {1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 5, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 5, 5, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 7, 11, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 1, 3, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 5, 5, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 3, 9, 7, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 1, 15, 21, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 13, 27, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 1, 15, 7, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 15, 13, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 5, 5, 19, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 7, 11, 23, 15, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 7, 13, 13, 15, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 3, 13, 7, 35, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 5, 9, 1, 25, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 13, 9, 35, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 5, 27, 61, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 5, 11, 19, 41, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 5, 3, 3, 13, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 7, 13, 1, 19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 7, 5, 13, 19, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 3, 9, 25, 29, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 5, 13, 23, 1, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 7, 3, 13, 59, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 3, 5, 53, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 5, 5, 23, 33, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 7, 7, 1, 61, 123, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 1, 7, 9, 13, 61, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 3, 5, 3, 55, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 15, 31, 13, 49, 245, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 5, 15, 31, 59, 63, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1, 3, 1, 11, 11, 11, 77, 249, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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    {1, 3, 3, 1, 17, 17, 13, 75, 163, 781, 421, 1573, 2519, 9243, 20693, 60909, 65661, 208125},
    {1, 3, 5, 7, 27, 57, 39, 79, 157, 415, 729, 3651, 3581, 9443, 6409, 45993, 99051, 140977},
    {1, 3, 3, 13, 1, 7, 109, 77, 423, 185, 97, 3719, 2355, 10593, 2421, 37339, 24961, 24305},
    {1, 3, 5, 13, 17, 7, 125, 43, 453, 43, 643, 3757, 3721, 16083, 20871, 26451, 95201, 29153},
    {1, 1, 7, 3, 13, 49, 99, 253, 59, 21, 445, 3677, 6683, 2165, 32367, 55249, 5991, 155033},
    {1, 1, 3, 9, 21, 9, 15, 219, 175, 631, 665, 2455, 4701, 10639, 13907, 26937, 58867, 259861},
    {1, 3, 5, 5, 23, 5, 39, 233, 27, 811, 1435, 625, 4703, 3699, 20763, 50047, 123875, 10129},
    {1, 1, 7, 5, 23, 1, 49, 223, 309, 691, 953, 575, 5279, 10515, 11519, 35387, 48417, 134001},
    {1, 1, 7, 11, 3, 15, 125, 109, 39, 713, 1823, 1613, 4347, 6839, 29511, 26865, 102077, 31425},
    {1, 1, 1, 7, 31, 43, 13, 221, 115, 993, 1155, 1641, 1063, 2065, 18909, 45769, 65331, 188455},
    {1, 1, 7, 13, 21, 9, 59, 7, 79, 217, 2009, 667, 7685, 14761, 20149, 44133, 41037, 78369},
    {1, 3, 1, 9, 23, 57, 1, 193, 77, 681, 1135, 3657, 8149, 3559, 25011, 55027, 121903, 240157},
    {1, 3, 3, 5, 31, 41, 59, 5, 159, 627, 1569, 23, 2311, 2239, 20811, 54931, 130949, 193071},
    {1, 1, 1, 1, 27, 45, 43, 1, 381, 801, 451, 1361, 1611, 5379, 27819, 8949, 4953, 222335},
    {1, 1, 7, 7, 7, 11, 101, 17, 197, 561, 297, 159, 7443, 7273, 819, 23487, 24927, 151781},
    {1, 3, 1, 3, 15, 43, 119, 193, 205, 835, 7, 689, 8045, 11167, 19521, 65075, 87265, 53669},
    {1, 3, 7, 7, 9, 51, 43, 209, 239, 415, 995, 4037, 1219, 2683, 30459, 36161, 111157, 184551},
    {1, 3, 7, 11, 27, 3, 81, 43, 407, 463, 231, 3545, 2691, 5235, 22053, 37233, 98757, 149111},
    {1, 3, 1, 5, 17, 25, 47, 185, 487, 403, 1063, 1445, 4457, 15443, 11693, 54823, 131001, 9813},
    {1, 3, 5, 3, 5, 35, 127, 253, 173, 491, 133, 3575, 1981, 12735, 26021, 61615, 74615, 159829},
    {1, 1, 5, 9, 13, 37, 67, 155, 317, 389, 603, 4061, 3527, 9315, 32331, 43145, 82511, 240133},
    {1, 1, 5, 1, 21, 41, 89, 3, 61, 627, 1301, 2073, 447, 8139, 2509, 52075, 50687, 240239},
    {1, 3, 7, 13, 25, 61, 117, 107, 175, 7, 1173, 561, 5777, 10525, 20713, 34987, 48005, 214361},
    {1, 3, 7, 15, 25, 31, 127, 147, 177, 881, 95, 2115, 4765, 10485, 9253, 721, 193, 222459},
    {1, 3, 5, 3, 3, 13, 47, 77, 441, 1001, 215, 2365, 3603, 405, 11401, 14523, 65755, 258229},
    {1, 1, 3, 9, 19, 29, 71, 153, 77, 613, 1815, 2033, 1821, 15497, 18805, 28851, 88247, 143115},
    {1, 3, 1, 11, 21, 19, 37, 35, 427, 887, 1977, 1961, 3619, 10739, 30115, 55937, 102045, 110929},
    {1, 3, 3, 13, 21, 27, 49, 15, 405, 629, 2015, 867, 2121, 13789, 19225, 22343, 105629, 123113},
    {1, 1, 1, 1, 17, 19, 55, 207, 507, 1001, 1753, 315, 2799, 8643, 1519, 4057, 16599, 222223},
    {1, 1, 5, 7, 21, 37, 63, 53, 103, 261, 595, 389, 6041, 11127, 23625, 61683, 80953, 255891},
    {1, 1, 1, 5, 25, 21, 81, 233, 79, 57, 1311, 3965, 7747, 687, 32149, 397, 4551, 37657},
    {1, 1, 1, 5, 9, 19, 87, 67, 325, 157, 317, 591, 1401, 8275, 20413, 39529, 75349, 183679},
    {1, 3, 3, 15, 9, 3, 83, 205, 195, 599, 829, 3109, 3705, 13991, 8781, 41555, 31689, 86933},
    {1, 3, 5, 1, 3, 9, 37, 235, 271, 883, 561, 1473, 7693, 177, 14113, 19507, 75221, 67517},
    {1, 1, 1, 9, 7, 29, 87, 189, 239, 429, 537, 1657, 6373, 2449, 17621, 19649, 77235, 102775},
    {1, 1, 7, 7, 1, 43, 69, 207, 241, 561, 1809, 3119, 4657, 15797, 18751, 52169, 105005, 172657},
    {1, 1, 7, 5, 5, 59, 67, 231, 27, 435, 1073, 2689, 229, 733, 1579, 52289, 110285, 76721},
    {1, 3, 5, 9, 31, 19, 87, 41, 489, 705, 1363, 963, 5865, 8237, 10295, 43169, 81561, 177209},
    {1, 3, 3, 1, 25, 39, 63, 255, 403, 625, 1601, 71, 6609, 4165, 21987, 31269, 25473, 17063},
    {1, 3, 3, 11, 19, 13, 101, 245, 17, 687, 1037, 3345, 7257, 13081, 5131, 29003, 72319, 223505},
    {1, 3, 3, 3, 11, 49, 107, 29, 463, 465, 977, 4007, 2121, 4821, 1465, 53725, 36783, 247057},
    {1, 1, 1, 3, 1, 43, 71, 49, 261, 965, 1041, 3951, 3791, 2503, 26009, 52039, 4639, 141281},
    {1, 1, 3, 5, 29, 45, 79, 33, 119, 491, 1403, 1637, 853, 5609, 29853, 16435, 117877, 58443},
    {1, 1, 3, 5, 13, 17, 109, 187, 201, 705, 235, 1485, 7673, 6335, 3341, 20451, 64697, 129519},
    {1, 1, 7, 13, 11, 41, 95, 81, 135, 783, 1293, 2095, 3599, 10175, 3205, 56915, 131, 19281},
    {1, 3, 5, 9, 13, 19, 53, 223, 283, 733, 1915, 3029, 2779, 8133, 28163, 37263, 91245, 1927},
    {1, 3, 3, 3, 1, 55, 41, 123, 209, 195, 1423, 2467, 3809, 11169, 23593, 8703, 40975, 175651},
    {1, 3, 7, 9, 31, 57, 31, 115, 415, 445, 557, 3971, 1565, 15223, 7799, 10463, 117387, 225127},
    {1, 3, 5, 11, 31, 19, 3, 63, 315, 501, 903, 1925, 3393, 16149, 11013, 15483, 70765, 279},
    {1, 3, 3, 9, 29, 21, 13, 227, 263, 815, 1259, 2549, 955, 9237, 16083, 38891, 31145, 731},
    {1, 3, 3, 5, 27, 23, 33, 189, 107, 655, 889, 1549, 7315, 13341, 12721, 59339, 54503, 91679},
    {1, 3, 7, 5, 15, 9, 1, 255, 451, 91, 1279, 2359, 5913, 5215, 23161, 29327, 45275, 206709},
    {1, 3, 3, 9, 9, 41, 75, 91, 87, 695, 335, 3375, 7307, 14095, 5359, 7815, 9339, 46387},
    {1, 1, 3, 15, 5, 47, 69, 231, 423, 255, 1335, 3395, 2799, 8955, 31445, 59849, 104955, 240587},
    {1, 3, 5, 7, 7, 9, 21, 209, 321, 5, 653, 2199, 3657, 6397, 20229, 32349, 54543, 47971},
    {1, 3, 7, 11, 31, 21, 85, 49, 197, 865, 53, 609, 1867, 14503, 12671, 61703, 39245, 8493},
    {1, 3, 1, 13, 27, 31, 119, 247, 209, 65, 1729, 1563, 1597, 1617, 26597, 50139, 108667, 77035},
    {1, 1, 5, 13, 3, 49, 53, 219, 71, 1013, 1239, 3725, 117, 9273, 8277, 32619, 45933, 71509},
    {1, 3, 7, 13, 1, 3, 119, 153, 79, 555, 429, 1221, 3725, 6073, 1295, 7187, 117709, 258911},
    {1, 3, 3, 13, 1, 13, 105, 185, 81, 989, 563, 3761, 6725, 4699, 10539, 50247, 95307, 211927},
    {1, 3, 7, 3, 21, 11, 45, 81, 495, 391, 1437, 3495, 3789, 13701, 9479, 42505, 22561, 135019},
    {1, 3, 3, 11, 7, 61, 65, 211, 269, 997, 385, 3843, 4905, 2939, 28551, 19515, 25177, 68137},
    {1, 1, 3, 3, 3, 47, 73, 127, 15, 977, 209, 1791, 4711, 6733, 29093, 36311, 13665, 240603},
    {1, 3, 5, 5, 19, 39, 29, 211, 463, 755, 1723, 397, 213, 14009, 22701, 7131, 35587, 183885},
    {1, 3, 5, 9, 11, 29, 7, 25, 381, 631, 1343, 2255, 2535, 3239, 7287, 14161, 69295, 85245},
    {1, 1, 5, 5, 17, 47, 19, 217, 289, 411, 1855, 323, 4109, 2601, 5835, 61909, 99333, 99959},
    {1, 1, 3, 11, 1, 51, 121, 207, 403, 993, 1171, 3451, 3389, 957, 22125, 9333, 110775, 54125},
    {1, 3, 5, 15, 9, 51, 13, 251, 203, 861, 321, 2017, 6933, 10785, 20089, 65213, 105451, 117319},
    {1, 3, 3, 15, 19, 63, 89, 217, 269, 723, 57, 1923, 4267, 4895, 2191, 21605, 62401, 11063},
    {1, 3, 1, 3, 21, 47, 103, 75, 167, 989, 1401, 575, 3717, 10373, 21321, 5487, 36063, 140411},
    {1, 1, 7, 15, 19, 29, 121, 197, 429, 773, 901, 1875, 291, 11395, 31459, 55041, 49263, 185143},
    {1, 3, 3, 1, 19, 17, 19, 21, 41, 885, 1665, 547, 5887, 6205, 3317, 59399, 125559, 82721},
    {1, 3, 1, 9, 15, 39, 81, 9, 279, 33, 1287, 3035, 5759, 10647, 3933, 20953, 3137, 30693},
    {1, 3, 5, 13, 3, 33, 33, 169, 233, 83, 467, 3719, 5617, 6165, 15631, 56059, 95541, 245233},
    {1, 3, 5, 13, 5, 21, 81, 9, 413, 247, 1307, 3363, 3383, 11525, 1259, 8735, 36507, 98359},
    {1, 1, 1, 13, 17, 49, 105, 131, 385, 309, 1295, 565, 8031, 15391, 31263, 52657, 102721, 212195},
    {1, 3, 1, 7, 13, 41, 21, 103, 237, 649, 55, 1565, 6327, 8743, 15457, 29975, 34165, 80839},
    {1, 3, 5, 11, 15, 31, 121, 219, 375, 159, 731, 59, 3205, 15039, 10023, 46209, 34619, 110253},
    {1, 3, 3, 11, 31, 19, 79, 185, 363, 635, 463, 987, 2681, 6405, 30077, 21173, 14213, 58095},
    {1, 1, 5, 13, 23, 37, 57, 111, 293, 553, 269, 3393, 345, 1983, 1097, 47217, 22281, 212607},
    {1, 3, 5, 7, 7, 33, 65, 61, 185, 411, 187, 641, 6437, 4625, 17547, 38941, 81119, 48651},
    {1, 1, 7, 3, 19, 25, 39, 243, 139, 465, 691, 713, 7879, 14539, 31669, 35871, 130681, 255929},
    {1, 3, 1, 1, 3, 43, 87, 13, 179, 835, 719, 1189, 7207, 5863, 6077, 20669, 35469, 211155},
    {1, 3, 7, 13, 25, 59, 97, 129, 151, 985, 739, 1919, 7729, 14057, 21721, 17603, 82797, 181319},
    {1, 1, 7, 7, 5, 3, 21, 141, 379, 257, 207, 597, 4051, 7563, 25481, 59427, 45449, 61159},
    {1, 3, 3, 9, 11, 25, 5, 29, 131, 603, 637, 189, 4033, 13099, 15219, 4447, 73501, 135795},
    {1, 3, 1, 9, 1, 49, 57, 227, 141, 543, 1499, 3525, 3127, 11191, 4071, 47003, 7431, 155137},
    {1, 3, 1, 11, 27, 31, 15, 31, 113, 135, 1251, 245, 6965, 14263, 5679, 55201, 121453, 132503},
    {1, 1, 5, 15, 7, 23, 67, 163, 57, 513, 1809, 1343, 6165, 199, 31169, 30803, 86705, 71103},
    {1, 1, 3, 1, 15, 9, 75, 143, 273, 797, 819, 4037, 2305, 4841, 15697, 41191, 38187, 174131},
    {1, 3, 7, 7, 3, 55, 65, 135, 423, 185, 299, 2221, 7987, 4223, 28183, 32273, 95941, 260297},
    {1, 1, 7, 7, 7, 11, 67, 109, 507, 673, 1555, 2537, 7553, 4659, 3945, 20839, 32539, 43053},
    {1, 1, 7, 15, 1, 47, 61, 73, 211, 397, 1785, 4063, 6461, 13725, 11299, 17565, 80063, 118271},
    {1, 1, 7, 5, 29, 27, 97, 105, 379, 153, 915, 2795, 4933, 6729, 21207, 9995, 70241, 85641},
    {1, 3, 5, 5, 23, 13, 41, 67, 127, 649, 1351, 3597, 7077, 4989, 14649, 17401, 70883, 239841},
    {1, 1, 5, 1, 19, 1, 83, 3, 425, 873, 1943, 3935, 4257, 14587, 11829, 55217, 21963, 39683},
    {1, 1, 7, 11, 15, 7, 37, 239, 337, 245, 1557, 3681, 7357, 9639, 27367, 26869, 114603, 86317}
    };

} // namespace at::native::sobol_utils