COEFFS[8053] := Vector(15976, 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6,3159,2940,6696,1188,6657,7792,5193,5720,3691,1060,7485,5749,7746,6398,6911,2695,7204,4213,1689,722,1123,668,6133,546,1900,3135,5307,5243,5850,5945,5128,5388,3240,2836,1998,4831,2639,2955,7218,2673,7470,3027,3600,158,3576,5809,2060,3794,4952,3070,5097,4449,3518,3300,6114,866,2407,3739,5251,2324,6237,2230,6276,1388,5136,7425,4411,2390,5922,1558,1855,2807,6154,5098,5286,7561,7541,4253,618,2873,4123,1624,3319,2829,1393,2886,1074,5741,3019,2037,989,3608,7769,1601,7754,7361,2608,5075,3447,2834,2585,5114,5534,4929,3470,5735,3078,7632,3738,7410,7967,6861,1361,6075,3424,4725,102,6959,5215,5842,6449,2104,902,3957,5486,4748,1152,5836,5681,3535,1725,3624,5337,4829,511,2179,2618,55,5340,2588,6825,4319,4765,4898,7735,6966,4146,5502,5847,503,7043,4309,452,5657,1105,3874,4789,3431,6756,7278,154,2011,1241,5209,3235,2049,3191,1048,1096,6390,535,7361,2308,3763,1211,3990,248,5716,1223,1123,3376,6275,4410,1191,6551,543,3690,5483,5244,2887,5405,7178,718,2772,4385,2144,4935,3341,4804,7255,3988,6762,3093,1532,2040,7594,7402,1479,2525,4808,2296,5817,3773,3219,4234,1292,4752,4250,5038,6886,4305,6045,7048,7127,4869,3217,1315,6266,1291,471,3050,5729,2222,4771,3454,6868,7659,446,1732,1723,4332,5079,6168,5812,666,3823,50,2886,7543,957,476,1958,3349,517,7433,6537,971,1851,1710,3993,4173,353,3118,1399,1070,3201,3682,6014,5872,6884,7834,731,6548,956,5519,2119,996,6697,4884,6898,6206,3397,5788,386,3760,1255,7799,4960,634,7765,998,5876,5330,6810,1979,7520,6462,4287,2500,1912,5741,3858,7304,2906,1719,1887,5765,7838,3284,7281,318,3629,2692,6160,2767,1863,1213,2246,2775,3230,820,5912,6730,1703,6961,5480,1221,1855,1754,375,4424,3628,7632,784,6301,6485,7147,3720,5872,5004,1535,6127,5622,6047,979,6799,2290,3063,5973,6917,5693,7982,650,2895,4067,3118,1239,6891,3540,5706,2042,3992,7479,1838,5407,5919,7423,1973,6750,1187,1474,3383,1861,11,7424,4638,5468,7535,317,2684,7485,7512,3610,6367,5180,2210,3100,7593,7319,7937,7094,1297,3430,4837,3222,4921,2139,5292,6255,4400,954,6040,2881,6190,1393,3468,5324,2197,1703,2086,4110,7622,7103,1595,7287,5150,3516,3143,7313,7210,4423,5523,93,5207,5801,2892,4264,6576,5112,3715,4329,1563,4116,1750,5763,5576,2902,2529,6724,704,7734,338,5543,4786,5203,2260,4285,3760,6967,7155,7787,6660,5276,2045,2547,6794,761,6677,3550,44,4632,5764,6845,1121,3069,766,1388,644,6525,3037,1347,3021,3940,4856,6722,7791,8011,6304,1649,197,7901,1156,1014,300,7596,3221,2654,1615,7666,6113,633,3001,706,5556,1572,4540,1735,5169,5683,7861,7734,2544,5913,1065,4221,2013,2154,2657,1072,1720,7985,7888,3569,1061,257,724,6764,2345,1011,4560,6371,3518,3549,3909,7228,2092,3425,2689,943,4331,2301,3547,7195,6557,4205,1829,2911,1272,3113,3111,4674,7400,1806,3855,289,2371,1437,4707,6067,7218,2464,729,7932,6161,216,813,5164,2687,1799,2710,1611,8015,7399,7264,4663,4877,5365,5868,6757,1564,1370,6100,2239,6657,3999,7582,4749,6011,5718,7496,6563,4454,7515,6105,3055,6926,2084,7484,3248,2529,5335,1340,3499,779,6560,6556,1514,4153,3249,7486,1441,2600,2351,5437,5147,5440,3863,324,1650,1174,707,7541,7771,3474,6186,7739,2397,4794,2417,2407,5671,513,6541,599,7429,2016,7864,2816,2441,7842,7171,882,6267,6181,5030,7510,4836,6546,4128,5805,433,5401,3060,2016,2279,6038,2891,2785,1624,886,731,5132,2295,1577,7435,4544,274,3250,3001,64,1811,7486,831,4427,4533,4895,7870,806,6343,6502,7395,1683,1984,1924,4908,8035,754,811,803,6822,5502,1101,5785,1873,3353,3636,6384,5995,5973,2019,1648,5709,4626,609,263,3061,7303,6197,4794,1387,3465,5678,2743,2561,4826,6520,2747,3425,3842,5844,3541,5307,3200,678,7430,4010,72,653,1428,3292,4669,7404,80,7153,2196,7488,2828,3921,6126,5226,2237,3814,7578,3544,4888,6335,2020,6954,2792,1520,6933,720,2678,5382,6503,4710,6039,3861,7349,1470,2765,5513,954,5215,115,4474,6225,1442,2082,7748,1666,5418,7318,4870,6352,8000,7815,5326,7605,6625,881,7888,7773,6165,7303,5223,6535,5986,7697,6953,6880,3968,3855,1540,8038,3718,4474,2240,5844,776,4519,2370,4852,2784,7048,2957,4090,7719,6835,850,7507,1580,4162,6675,2862,2499,2178,2524,6074,4532,4084,140,2332,6389,5719,1135,2384,5927,4275,922,449,5360,6505,6662,4136,3567,5466,1082,3704,778,6160,1563,7963,872,5438,4321,1028,1912,5215,2832,1401,7900,2735,4913,5670,5760,4776,7848,5170,4168,6204,7432,5501,4346,4627,284,3581,3511,781,4175,1834,1709,3382,7498,3808,6619,5357,359,7482,1022,4428,6643,999,5433,5465,6395,7831,1887,1411,42,3869,458,7691,3239,6832,6037,7645,4252,5261,4257,1458,2859,4122,5166,3275,5962,313,7487,6643,11,3058,816,4163,2896,7735,5056,3819,7833,3226,702,6984,7561,1130,3004,1703,4356,3609,7785,6609,62,7611,3753,7169,5104,7518,5235,3186,5886,3516,2360,2349,5780,1339,7985,4124,6094,2253,387,3730,977,3360,3273,262,7444,3875,228,7052,4626,3549,2087,567,386,6406,827,7958,7549,30,1246,7319,6813,6835,2867,6316,4389,3063,3920,8043,3484,7021,1318,3564,4830,399,6343,7924,4607,4225,1201,6227,3841,2351,3034,7728,978,245,702,3765,916,3608,7984,6870,3769,5256,287,8011,6759,3462,3010,4099,4006,5426,2576,17,2742,598,3797,3306,5301,6470,5895,2199,7290,1716,710,5392,6533,551,6343,5137,1090,3417,4862,2843,7758,3908,5724,5822,7412,8042,3587,6805,5110,6847,4090,3665,3431,3962,1330,3888,2343,2521,7154,7955,2857,5616,3729,2285,6466,2873,7879,7056,7142,2677,4704,6435,31,1916,4133,7998,7794,7642,4853,6808,7567,6549,5722,609,1023,6308,523,1426,4228,1903,2872,7173,7281,5746,5520,4430,6031,1974,2922,4347,4841,4418,4832,7317,1249,4915,454,7358,1545,6835,3369,6664,6041,7752,7322,2748,4219,5415,4424,4723,6709,2157,4709,61,3922,3507,4418,7877,6841,312,7513,495,1113,2113,1469,4446,825,384,7186,3211,1283,1294,5274,1883,2621,1193,1307,827,2207,382,1481,7274,6216,5302,934,772,659,4042,4678,6857,1907,3798,707,6881,1689,4426,1583,3312,2667,4971,424,2910,2197,4699,807,5047,7056,4436,7314,2977,82,1288,6307,3869,2313,4625,4530,6868,1637,2345,5054,6520,6978,6220,1587,2573,3617,2147,7675,5251,7706,1216,6350,5781,3296,6262,6328,4194,6787,7878,704,874,4149,2039,2566,2756,7174,4536,3313,7302,6648,6596,768,1129,4603,972,3592,2913,1856,4708,3651,7609,412,2779,1388,152,71,6779,7610,6169,1065,3356,2299,6705,1617,1657,1863,7165,1297,107,4800,2808,4193,5763,1489,5925,5005,1991,5120,5864,789,4708,3923,6054,2933,6068,3815,6275,3903,771,4328,6890,1158,2484,3661,45,6161,6254,4465,7648,5638,1327,195,3523,7495,6508,688,5562,5915,7432,3876,4206,4777,1028,6353,7799,480,6155,4010,2555,5687,3189,277,6693,7464,6894,7274,6275,5253,4231,796,7315,3214,912,8049,1235,2675,1703,103,4406,1656,3039,1942,7215,442,7757,7125,2305,4026,1440,1981,965,6838,2565,1397,5204,2887,6530,4240,478,948,6562,8022,1346,4955,6912,7035,5318,2784,3438,2681,565,4196,7597,499,1409,1539,6808,2347,8016,863,1333,1424,3834,3479,1880,457,6018,6911,2401,7587,2130,5714,4160,5399,6245,7558,3371,7807,1903,2055,1052,2262,7727,1346,1675,2303,120,7192,2069,5962,3950,7336,976,5869,8000,5976,3146,8025,4011,3065,1820,2580,1995,4969,489,1424,5441,2334,1076,2693,2666,6118,1210,4581,5288,2250,2843,3701,6639,6206,921,2562,1477,2353,4885,2668,5529,3461,5519,4268,1477,864,7175,5598,2904,2233,2331,1292,6004,3127,5795,4109,3936,5355,4704,7597,797,7362,5362,2312,6346,5880,5946,5338,2479,3948,4092,7932,6297,6839,1649,5522,4879,4503,6646,4418,6279,7087,2674,4806,6413,6486,7510,7610,2321,3806,1068,3782,2107,5128,2566,6467,5388,2642,5448,2096,2174,4102,7053,5351,7616,6818,1584,259,5760,3699,6288,3361,5851,1864,4896,6120,417,7950,4045,5592,4079,3895,4080,3318,2592,4873,7579,8039,6086,5001,4905,8023,6435,6362,7210,7766,5004,6931,4648,927,1181,153,4556,3484,777,5286,3359,4036,7260,3713,7503,7170,6503,3434,7250,5165,2904,2699,7178,7314,4460,3164,1088,7309,5557,852,4926,1290,3998,3510,4758,3952,4148,4983,4807,6998,2456,3414,707,7062,7256,5708,6195,2069,7738,342,767,2810,651,1030,7806,6427,3761,6291,5241,2368,5437,5159,4130,2985,7093,7002,4427,3466,2555,2364,7803,7052,7828,6052,1306,5199,4379,4849,7979,5017,287,7531,861,159,144,2435,2718,5490,3376,4790,670,1746,5843,4810,3674,5361,7793,5400,488,4929,2066,6311,4977,4687,389,5088,3985,4484,5215,4808,5343,3400,2649,4271,3385,1994,7622,342,7553,7225,8026,3359,7468,2748,6738,1594,6616,948,3102,3618,1989,7028,2537,5972,1579,3781,6317,571,6394,3858,6023,1853,4183,1129,3920,2966,8035,1170,7194,2587,369,5482,5964,6045,7627,2497,7871,1420,7429,1487,1822,1094,3095,4198,3660,7781,849,3500,6621,662,5497,1548,7239,4481,4568,3907,7249,7882,6555,5928,5072,8049,2080,1597,5033,3103,1161,2420,4698,232,7528,4795,3751,604,4002,2640,5872,3546,7915,7153,7231,3107,4599,5383,2515,6454,5465,1009,2575,3383,4914,4294,5930,5386,7638,1210,7021,2135,5809,2781,6060,6728,5486,3560,4977,5740,3184,2482,2018,5071,2694,6567,427,3356,203,7735,442,6191,7968,2009,3943,1521,7882,7261,3552,3891,1538,1325,1776,4945,4033,7436,3031,6264,4022,3160,7473,6191,3228,7387,2151,2141,5098,617,2740,3356,4328,4229,5348,1466,4111,3388,5717,1807,2122,1922,6018,5522,4682,7464,781,6805,5433,4035,4997,2278,1761,7004,2346,2053,4536,2006,5778,2841,6444,3774,4910,843,5172,7548,916,4856,6303,7441,4030,5609,555,4149,7142,1235,1082,1471,1240,4865,1476,2663,5689,6117,74,1793,7267,4010,5235,904,5008,5659,4588,5184,668,6835,168,6911,7815,7849,5684,3406,6259,2542,5642,3921,293,2040,3653,4940,1090,5134,3287,6299,1577,2304,521,2846,468,6676,1139,7204,2665,6528,3575,5923,3220,2730,6511,5069,7669,5838,18,4947,1555,7550,1990,1912,1659,2623,104,7785,3782,6878,7008,3081,7359,4740,7398,5614,1379,7121,4622,7156,3189,3730,6894,6075,3746,3589,7953,2201,69,5513,2481,1116,2851,3316,1599,7498,4826,6906,1164,7021,3990,7832,7418,3296,603,5226,5435,2331,166,3083,277,6796,7767,2272,2216,7873,1528,5356,5667,4694,2808,6040,4993,4395,4630,458,1841,6888,6999,6940,4267,5279,186,445,2278,4593,6797,1333,5629,6883,1416,4948,1451,5182,1314,2355,3338,3474,6899,2738,567,4909,4362,1394,3628,5272,6194,6697,7180,732,2058,6938,6279,6211,6823,7908,7682,6768,4241,4784,7480,5770,2139,5230,93,5164,5794,2789,2940,3439,5963,7043,7324,4643,1963,6767,1072,3690,84,6111,360,3956,1093,4567,5527,1585,5568,1695,1078,2347,6181,4068,2468,7007,2111,7949,6673,6656,7291,7535,2025,1009,3403,5268,6523,5643,5824,7840,3213,5050,6593,505,7200,1665,1479,5122,2492,7350,6657,5626,7702,6007,2457,4465,6059,780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