COEFFS[8647] := Vector(15976, 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880,802,8472,3471,4793,516,5048,4267,801,4202,990,1454,2037,1057,6436,4358,5089,3038,6616,416,3733,3523,372,4701,2511,6585,7390,4478,5284,2673,8453,3682,371,7800,7143,5162,510,8501,7056,6525,5901,594,1260,6693,7839,2706,5944,1239,4912,5714,791,8361,4067,8403,4409,6648,2280,7452,1683,5384,7865,1022,3673,2018,2364,7731,5394,3982,2734,7729,3340,7495,2783,8148,6949,6341,7685,4484,342,158,5195,5660,5590,6483,6795,992,7530,4942,2422,5240,2282,7209,4279,1747,6579,8082,4618,802,2779,6096,643,6442,6695,6674,1386,5937,5381,763,3477,4233,1072,4781,5924,6422,3484,2835,7958,3922,6706,2435,6535,5221,7758,7571,4144,6996,726,7203,6504,4014,7520,3582,5735,8412,1353,2593,5627,2644,2131,4748,1867,4721,2034,6026,5845,4359,7115,4083,3472,1575,8372,8445,5110,5194,4807,3168,5641,481,4380,1138,3567,8368,4394,8540,6507,742,6135,8210,5379,3727,5852,1790,256,1178,229,3000,5073,1395,4314,1536,8412,3662,5473,1184,6370,598,6277,8291,2326,5531,559,7207,6032,6225,2723,2324,747,8144,4273,6215,314,5563,7408,460,6308,1757,7926,6655,5789,8086,7669,2210,7574,642,922,6224,6724,2058,7368,964,780,7216,5967,5711,5569,6376,776,2983,1776,916,7010,171,4205,66,4110,6181,2960,1196,8015,994,3905,759,2042,3611,2856,7853,2482,4713,4396,4285,2816,8271,6633,4680,1405,3207,2103,6523,6201,6368,7071,6898,1066,5161,4781,2018,5571,979,4810,8512,1236,533,5579,1711,8602,6418,7087,4388,3369,1843,2508,6437,4531,6328,5879,5163,2198,1123,118,6081,7276,4955,5432,6729,6838,5667,463,618,2617,3931,406,2386,5877,2507,335,5717,8220,8306,8449,7631,401,2301,2964,3266,703,1057,1938,2593,3002,837,7905,4347,3666,512,3794,6244,4301,5820,7668,724,7562,5172,7961,5016,8365,6855,6174,144,4725,5928,4966,2029,919,3571,8061,2615,6481,4259,22,2310,1962,6879,6267,753,6460,1224,3540,1180,5827,2547,8552,7897,8364,63,1187,1113,1805,3914,8221,387,3375,6891,3257,3723,91,3965,1571,2251,3305,6815,7844,2602,6640,5594,1581,5916,4023,2561,7544,8478,2918,8461,2131,5598,954,4956,2414,6873,4920,7593,8444,1976,3050,7945,6752,5438,7452,4762,8104,8590,4030,7784,5364,7845,637,4862,1560,6660,7977,3484,462,6065,5818,2029,1632,4112,660,812,7360,4942,2819,4357,7531,1195,2029,3282,6091,7317,3173,8360,161,2016,7363,6244,7355,201,6409,317,4778,190,5194,2171,4050,7908,1774,7904,1158,3475,6289,214,6473,8585,652,2005,7937,3993,7938,1937,8586,4281,7856,2039,487,1481,4164,5640,7665,4931,126,6800,900,7138,5020,66,7736,5498,7018,2130,4335,7148,3699,3585,6706,4097,7356,566,2984,508,866,120,4576,149,8231,2838,3381,1275,7068,2807,7190,3333,5113,5346,1035,8531,2230,6355,57,1847,886,1398,7760,8134,7181,6970,3966,2979,7575,8272,2011,3629,3234,4528,3654,9,3845,1364,5832,2710,3014,4192,3182,6334,1238,1238,82,8511,4617,5223,7099,287,6766,6473,1916,2261,4407,4332,196,4155,311,5601,4204,492,4387,3235,2598,670,5957,301,8207,6508,8041,5553,1521,8057,2269,5234,7814,2556,3172,1245,7418,7682,4414,7758,7117,4239,4955,3935,2322,6329,5986,5925,1939,464,2503,2266,1942,388,6920,2147,1184,3791,6303,7336,2923,8557,3352,5487,4552,2078,4720,6482,7365,4740,6471,394,4854,2859,5022,107,2012,8644,2648,4532,8196,6350,1093,4184,2361,3835,2361,1764,2661,4270,4867,2123,8528,4821,1757,1876,7708,3803,3758,4973,4132,4850,6574,8356,5661,623,4187,6132,5431,3389,841,739,6690,7045,5290,1606,886,328,348,4465,4251,3104,3765,785,4452,8600,7559,3261,5354,5829,4964,5352,2005,226,8465,5478,1808,4634,7476,3674,1122,1909,8335,7408,2779,3689,8507,2500,4753,8543,2820,1105,592,4917,6671,1161,5216,8390,6981,1338,8348,682,1375,6813,4123,2969,2082,921,8644,1062,6579,1041,3949,2718,2733,2169,6907,2561,6178,1534,6276,2314,2019,1226,5853,7323,533,4135,6297,4266,3226,6564,1133,3812,4812,8365,5687,5730,333,6928,4645,6982,1769,2506,1927,935,1498,3060,2342,1677,8168,4145,8342,3426,213,6677,7982,5697,1741,8591,5064,6090,5855,7758,3912,3651,7456,5715,8133,7007,6955,278,1603,1442,8541,2282,5952,499,455,7658,3584,7217,637,2778,8254,1966,1236,2579,6818,4348,4813,2403,5779,3532,7128,2415,7982,6643,2381,1076,8197,4661,5649,2393,8260,496,3267,5610,7039,6153,1958,5684,6181,5054,1880,2490,7874,80,584,3640,79,4069,1654,5090,5936,940,2011,6819,3765,5780,8620,4764,3463,3791,1891,4394,4941,276,2612,7491,5386,4317,399,8040,8448,4626,947,5140,7448,2676,5126,662,5033,3437,867,4715,651,2248,1380,3402,4443,2856,5807,4259,1237,2709,7003,3090,2157,2764,7358,2955,2520,6401,4192,7342,5187,3955,2172,4563,1949,3688,7101,1845,2283,6661,5889,8054,7902,3442,3807,3169,4518,4471,4144,893,5924,2580,8324,5510,4389,1005,6007,4128,2842,7524,6732,6514,5698,8327,4553,6193,1012,2465,5098,4755,5444,4004,259,5249,6270,6336,26,8283,3419,7960,3307,222,2421,2381,586,4284,2848,3686,5044,3963,3340,8553,6810,6065,6596,6937,8172,6966,6703,4683,825,7213,5612,6650,7466,2297,191,565,5561,4232,867,8463,3008,1266,8583,3618,176,2355,4639,1330,7647,2975,8612,2030,272,679,1185,2669,6280,2048,7668,8495,7299,3284,1898,8118,6385,2534,1835,5824,2608,5519,5617,5247,8359,606,707,1700,2918,6050,994,3231,8330,326,1299,4788,1918,8083,87,102,4503,1403,6159,1106,2264,7560,7873,4175,5037,5069,2239,3428,4847,4557,842,4699,1894,7500,7437,3038,3878,5412,2048,6166,7946,6062,604,1978,5007,2843,3449,2697,1280,7827,2129,8245,8000,4300,231,4367,4432,6196,3711,1351,3091,7929,654,454,522,6611,4193,2964,676,5102,5977,6937,6495,1255,2969,2731,6254,3142,7956,4033,5116,7802,92,737,3231,5811,5729,5469,2404,988,6389,1071,1536,4328,7492,2325,5066,8395,7635,2388,8510,2140,6374,2921,2667,7839,1222,7033,5079,1160,6022,1050,1928,134,3345,5487,522,3104,6718,382,791,3450,4539,2584,7467,5510,6744,940,6852,8336,5118,3303,616,3448,4663,3387,6115,3425,1622,3144,1157,6195,636,7678,5606,6466,1907,74,7854,4498,3106,829,3986,8584,4312,5010,7265,6959,6620,4668,5206,6417,1097,1578,4072,2277,1575,5061,402,3858,6979,6969,2861,599,3190,4519,3328,6707,7659,78,3209,323,7374,2800,7977,212,6771,3452,6680,629,7669,4946,8521,3011,6369,1236,8384,81,2685,8343,3070,2163,3948,7329,4887,1131,7592,2270,6425,2569,839,950,4261,673,5387,7021,7639,3477,7403,337,1661,418,243,1720,176,5796,1561,1223,883,6143,4059,298,4234,2519,2616,4550,714,6625,6187,1496,5673,5328,1049,3993,3918,5828,7700,1616,1299,5836,56,6292,2980,2587,7307,6172,7088,2030,4440,5210,345,1289,7386,4420,6945,3552,4835,698,560,1768,2483,5185,703,5148,8360,1154,586,1549,8316,7163,8201,6938,1107,4542,3085,3593,6730,7773,4963,7444,3936,3534,6140,2603,4506,2785,7993,4543,2064,61,22,7624,5007,3106,920,2764,1087,4580,7673,6631,5955,7876,502,8393,596,572,5809,2497,5291,6660,4515,5091,1486,361,5396,6176,1102,4475,993,661,5338,5194,4478,5491,4514,910,6835,3747,5844,7907,1887,5117,1193,4501,2505,1828,7552,6022,3540,5990,3389,2706,6853,5270,8203,1139,7499,6582,131,4021,3038,3490,8367,5145,5847,5617,8185,5409,4920,7510,1934,2605,7983,3272,725,3870,6945,101,3841,5127,8054,7711,1121,1812,4923,7339,4638,5753,4247,16,2849,1444,5501,7000,533,6020,976,6313,550,7251,6738,231,5177,4130,2683,6905,4785,4364,1991,1942,8549,5664,4971,4677,6550,6492,6665,5538,1566,2707,6639,2025,5673,4573,5832,6071,2693,6910,6656,3754,6439,3398,7983,1903,5128,1346,2576,6038,5953,7886,7953,385,2659,3226,7019,5938,3637,8480,261,2345,2689,5919,5915,649,6792,7511,882,2877,3271,5153,8168,168,1014,3517,849,739,2075,5508,1268,6740,1411,417,500,2728,8072,6299,7278,2646,2642,2806,838,2550,3256,3814,1747,916,6403,4984,5445,4610,6405,3754,816,6409,6646,6487,2433,3796,8415,8003,5545,364,6232,3701,6644,4797,1008,8259,4098,2572,5463,5875,3419,58,6035,6217,2009,5891,5012,7350,3960,8177,2040,3846,8628,1839,6756,5365,8217,3136,517,3671,209,2107,6781,2403,3605,4405,506,2262,7783,1170,2605,7848,5821,3013,7158,2599,7965,5287,4412,654,3520,3569,5606,3298,4726,504,4270,7465,3400,1887,8264,737,6685,1653,4105,3949,6408,2711,8585,1709,1048,4377,384,1254,970,4790,4321,2145,1875,5313,5444,4794,2428,5435,1477,3929,3843,7840,2008,2651,977,2289,2635,142,2257,8056,5272,110,6251,2145,24,515,1915,5620,5301,8579,438,2476,2379,3592,4045,8592,537,2769,7002,2184,5180,7410,5320,5272,6976,7680,5446,5116,7282,19,1733,596,4955,625,3630,8552,6895,2019,343,1257,2056,1192,6499,3837,3092,6471,6547,1019,3679,379,2492,3494,7565,6394,8234,4817,6877,7311,4211,8025,2892,1214,2452,6884,632,5444,6884,5819,3156,6861,997,1545,6016,5436,300,6899,1362,7936,2067,5235,7021,3711,1899,5025,1445,6261,7665,6503,2876,4562,8580,7587,8076,2668,2931,7767,7708,5501,2525,8572,95,18,7182,3075,3584,3434,7711,1724,1568,5943,4408,1510,7580,6361,2429,4834,1882,7528,5273,7757,1768,3496,6572,6190,908,7337,3759,5076,3234,3356,8475,6801,5797,6732,1793,6331,7073,2542,5296,3182,5425,6681,3957,2737,733,6228,2758,6632,1153,2810,5261,3046,6368,1865,7764,5635,4525,8282,4336,5308,6656,2485,4765,6882,3793,8372,5473,3099,6244,981,6709,7005,5080,4211,7041,4570,1840,7157,160,1998,2923,2374,3248,2568,5411,2929,3443,8346,5287,1447,617,7191,7967,7523,5010,6899,4136,2157,1217,5541,7825,5157,7087,7183,1491,8342,7617,6282,6526,3933,2041,3805,5338,6499,3092,4196,4331,4729,79,3196,5717,6064,3427,7512,5111,5195,2613,848,5115,4619,221,4325,469,2429,6490,7000,7289,4184,5831,2307,6569,7473,4831,4469,8259,3804,7231,6723,102,1039,4555,6690,3318,3373,3159,2086,5629,3136,1462,1983,496,5033,6959,7926,331,2076,6609,4163,6158,8500,7870,5729,1079,2827,876,5986,3920,1374,7859,6445,7120,7495,6887,5937,1609,6538,3437,484,7107,3309,4538,1966,5465,3435,828,7616,5142,8155,7132,78,2657,2553,7756,3783,6547,7249,6766,1151,6991,5972,7380,2095,6136,2402,6487,3556,2485,4924,815,1627,7220,2038,2636,4412,5707,6890,2737,7323,3562,6822,2048,2433,6736,2739,5051,885,3741,6612,6009,2500,1463,6948,5272,7085,6104,1698,8510,6434,192,2782,1037,3234,7877,108,1856,5803,2558,5267,150,7009,4273,8498,4061,3168,4280,441,7183,7533,8032,6153,2804,6036,1277,6794,7837,8117,8500,1429,2591,4304,486,5750,8010,5007,7898,2331,2073,5000,602,848,1528,6402,3730,2422,7370,1395,489,310,1710,1600,1267,3154,2678,1079,8506,4969,8389,7619,4239,1214,6125,6743,3630,4361,7900,7728,6826,5117,6796,6234,1798,7585,346,3863,7901,763,3063,423,3857,4125,5664,5238,322,3864,623,2194,927,2052,5003,3441,6265,7415,6150,2506,5700,3899,483,7165,5836,7606,3951,2552,5315,149,7877,8509,8642,1196,19,3298,4002,4278,3861,4236,4797,216,6766,7153,792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