T=80;
N=80;
M=500;
P=[|8695,188,27,372,259,425,139,269,371,213,108,311,6432,139,34,232,472,65,357,431,222,380,243,244,142,6627,239,263,34,32,441,117,302,3697,212,394,61,3520,43,845,5745,44,321,92,451,406,60,2197,196,6004,257,494,298,7250,7,1117,213,116,192,416,74,245,419,287,171,1603,436,5,9961,205,490,183,9009,387,9473,169,336,5766,434,283,
|8799,188,27,373,261,433,139,272,377,214,108,315,6517,140,34,233,481,65,360,438,222,386,245,246,142,6674,243,268,34,32,442,117,305,3762,215,399,61,3596,43,860,5752,44,326,93,456,414,60,2232,196,6079,257,181,302,7319,7,1117,216,116,193,418,74,247,424,292,173,1617,438,5,10000,207,496,183,9042,393,9525,171,342,5801,439,286,
|8826,189,27,379,263,441,139,272,383,215,109,319,6638,140,34,233,484,65,363,440,222,391,249,250,143,6749,247,268,34,32,450,117,308,3827,216,402,61,3629,43,870,5815,44,327,93,456,418,60,2256,197,6191,258,182,303,7372,7,1126,219,117,194,419,74,251,428,292,173,1628,443,5,10000,209,505,183,9152,396,9648,172,345,5873,443,289,
|8897,190,27,379,267,448,140,277,385,215,110,321,6655,140,34,234,493,65,368,443,222,393,250,251,144,6787,248,271,34,32,455,118,313,3900,219,403,61,3680,43,887,5944,44,330,93,464,419,60,2276,199,6299,258,185,306,7528,7,1136,221,117,196,419,74,253,435,294,175,1630,447,5,10000,211,509,184,9207,398,9698,174,351,5998,448,292,
|8987,193,27,384,272,454,140,279,387,217,110,324,6740,140,34,235,500,65,375,449,71,398,252,255,145,6820,252,275,34,32,459,118,316,3948,223,408,61,3749,43,896,5992,44,335,93,473,420,60,2284,199,6349,262,186,306,7554,7,1145,223,118,197,427,74,257,443,296,178,1651,455,5,10000,214,511,184,9279,401,9900,176,353,6000,457,293,
|9175,193,27,390,275,457,142,284,394,219,111,328,6858,141,34,235,507,65,379,449,71,399,255,256,145,6846,254,277,34,32,465,119,322,4013,226,409,61,3801,43,915,6053,44,339,93,473,422,60,2321,201,6460,263,189,309,7644,7,1168,224,119,198,428,74,261,448,297,179,1676,460,5,10000,214,514,185,9427,404,9924,176,353,6013,462,298,
|9347,193,27,393,275,464,144,287,397,221,112,328,6917,143,34,236,516,65,380,458,71,406,259,258,146,6884,257,279,34,32,469,119,328,4045,229,409,61,3861,43,923,6104,44,340,93,475,429,60,2371,201,6511,263,189,310,7778,7,1178,228,119,200,428,74,263,454,301,179,1691,466,5,10000,217,520,185,9475,404,9981,176,358,6057,465,300,
|9533,196,27,401,277,473,146,288,403,2,112,330,7004,145,34,239,516,65,380,459,71,412,262,259,146,7005,259,279,34,32,472,120,333,4087,233,410,61,3895,43,936,6152,44,341,94,476,436,60,2406,204,6568,266,191,314,7953,7,1200,232,119,200,435,74,266,455,303,181,1701,474,5,10000,219,521,185,9587,408,10000,177,365,6085,470,305,
|9681,196,27,401,170,476,147,290,407,2,113,331,7031,147,34,240,517,65,380,462,71,415,264,262,146,7049,260,279,34,32,473,121,334,4154,234,414,61,3948,43,937,6223,44,347,95,484,437,60,2449,206,6601,268,194,319,8022,7,1220,234,119,200,435,74,271,461,307,182,1704,475,5,10000,223,530,187,9643,414,10000,178,366,6175,477,306,
|9821,1,27,405,172,481,147,295,330,2,114,334,7122,149,34,244,518,65,381,471,71,417,265,263,147,7051,262,282,34,32,481,122,340,4199,237,420,61,4023,43,951,6276,44,353,95,484,444,60,2458,207,6620,269,194,322,8100,7,1224,236,119,201,444,74,272,466,307,183,1720,475,5,10000,226,531,190,9822,416,10000,180,366,6194,480,312,
|9969,1,27,410,172,490,148,298,334,2,114,337,7217,150,34,245,526,65,385,471,71,421,268,263,149,7064,262,283,34,32,484,123,344,4219,241,423,61,4053,43,955,6371,44,359,96,485,444,60,2493,207,6722,269,195,322,8169,7,1247,237,119,201,449,74,275,472,307,183,1752,483,5,10000,228,534,191,9829,420,10000,182,372,6267,485,315,
|10000,1,27,414,172,493,149,303,338,2,114,339,7238,152,34,249,529,65,385,479,71,422,269,266,150,7215,262,287,34,32,494,124,345,4314,242,427,61,4144,43,972,6445,44,359,96,490,444,60,2526,207,6761,273,196,328,8352,7,1258,237,120,204,449,74,278,480,307,183,1754,492,5,10000,232,534,191,9943,428,10000,184,374,6311,495,318,
|10000,1,27,421,172,498,149,307,339,2,114,340,7244,154,34,249,532,65,391,486,71,424,273,266,150,3176,266,288,34,32,501,125,350,4371,242,433,61,4238,43,974,6550,44,359,96,500,450,60,2567,207,6783,277,197,328,8398,7,1279,239,121,204,455,74,278,488,307,183,1759,492,5,10000,234,534,193,10000,431,10000,186,379,6426,501,320,
|10000,1,27,427,174,503,151,308,342,2,115,346,7297,154,34,250,539,65,395,490,71,427,275,271,150,3178,267,292,34,32,501,125,352,4449,245,439,61,4277,43,981,6600,44,365,97,501,458,60,1361,208,6928,279,199,328,8468,7,1307,243,122,207,459,74,282,494,310,184,1770,498,5,10000,238,541,194,10000,438,10000,187,385,6428,502,326,
|10000,1,27,429,174,509,152,312,345,2,115,351,7364,155,34,254,539,65,332,500,71,428,276,274,150,3246,267,293,34,32,501,125,354,4515,245,441,61,4317,43,996,6707,44,365,98,501,464,60,1368,210,7058,284,201,331,8492,7,1333,244,123,209,467,74,283,499,311,186,1798,503,5,10000,241,547,196,10000,442,10000,187,390,6488,503,327,
|10000,1,27,431,175,513,154,314,345,2,115,355,7410,155,34,254,540,65,332,502,71,435,280,278,150,3287,268,296,34,32,505,126,357,4597,249,442,61,4356,43,1003,6753,44,365,99,502,471,60,1387,213,7216,286,203,335,8551,7,1357,246,124,212,474,74,288,502,314,189,1819,511,5,10000,242,555,197,10000,449,10000,187,392,6510,504,327,
|10000,1,27,439,176,518,154,315,349,2,116,355,7446,157,34,258,550,65,334,509,71,442,282,280,152,3291,273,301,34,32,511,126,362,4673,253,451,61,4451,43,1020,6805,44,370,100,505,480,60,1396,213,7361,287,204,336,8716,7,1376,247,124,213,475,74,293,503,318,190,1819,512,5,10000,243,556,199,10000,455,10000,190,394,6563,510,327,
|10000,1,27,446,178,519,155,321,351,2,117,360,7612,158,34,262,558,65,334,517,71,451,284,282,153,3354,276,303,34,32,516,126,368,4693,255,457,61,4552,43,1033,6898,44,370,100,505,481,60,1397,215,7503,292,205,336,8882,7,1406,249,124,214,475,74,297,509,323,192,1826,518,5,10000,244,562,200,10000,464,10000,191,396,6636,518,328,
|10000,1,27,452,180,522,156,325,357,2,118,361,7627,158,34,263,560,65,338,522,71,453,287,287,153,3405,277,308,34,32,523,127,368,4702,255,457,61,4624,43,1054,7054,44,370,100,506,482,60,1398,215,7617,296,205,340,8918,7,1425,251,124,216,480,74,302,517,326,192,1834,528,5,10000,246,564,201,10000,466,10000,191,403,6703,519,331,
|10000,1,27,460,181,522,156,331,357,2,118,366,7788,160,34,265,564,65,340,527,71,462,290,290,154,3456,280,308,34,32,532,128,371,4764,259,459,61,4692,43,1064,7101,44,375,101,516,482,60,1409,217,7683,297,208,345,9113,7,1443,251,124,216,485,74,305,517,329,195,1856,528,5,10000,248,565,201,10000,466,10000,193,404,6788,522,334,
|10000,1,27,462,183,533,156,335,362,2,118,367,7890,160,34,268,574,65,344,531,56,468,290,292,154,3509,281,310,34,32,533,128,376,4814,260,464,61,4773,43,1079,7107,44,382,101,518,489,60,1415,218,7748,298,210,350,9270,7,1454,251,124,216,487,74,311,522,333,197,1879,39,5,10000,248,568,201,10000,469,10000,194,410,6827,531,338,
|10000,1,27,464,184,537,157,339,369,2,118,372,8034,162,34,273,575,65,347,539,56,475,291,296,154,3509,281,316,34,3,541,128,376,4835,262,472,61,4818,43,1081,7183,44,389,102,522,497,60,1443,222,7881,300,210,355,9476,7,1456,253,125,217,489,74,313,525,339,198,1888,39,5,10000,252,573,203,10000,472,10000,197,417,6843,541,342,
|10000,1,27,470,186,542,158,344,374,2,119,373,8150,163,34,275,575,65,347,542,56,478,292,301,154,3514,283,321,34,3,544,129,379,4882,266,481,61,4865,43,1100,7304,44,393,102,531,505,60,1445,225,8011,303,213,360,9498,7,1475,254,126,220,495,74,313,528,343,198,1919,39,5,10000,254,585,204,10000,479,10000,197,421,6981,550,344,
|10000,1,27,474,188,553,160,346,374,2,120,377,8300,165,34,277,576,65,350,553,56,487,294,302,155,3587,284,323,34,3,545,130,386,4990,267,481,61,4866,43,1121,7435,44,400,103,540,515,60,1463,225,8144,308,214,367,9573,7,1476,258,126,221,500,74,317,531,348,198,1940,39,5,10000,256,592,207,10000,482,10000,199,427,7076,550,344,
|10000,1,27,479,188,555,162,352,380,2,121,384,8466,165,34,280,576,65,354,555,56,489,295,304,157,3634,286,327,34,3,551,130,389,5016,270,491,61,4950,43,1127,7581,44,402,104,547,524,60,1495,227,8252,309,217,370,9733,7,1490,258,127,222,506,74,323,542,355,198,1961,39,5,10000,260,595,209,10000,488,10000,199,433,7214,561,347,
|10000,1,27,489,188,565,163,352,381,2,122,386,8608,167,34,285,584,65,357,555,56,499,300,305,159,3686,291,327,34,3,561,130,396,5050,275,492,61,5043,43,1142,7607,44,408,105,555,534,60,1521,229,8431,309,218,371,9950,7,1504,260,127,222,509,74,328,543,362,198,1964,39,5,10000,261,606,212,10000,489,10000,200,441,7310,565,353,
|10000,1,27,494,191,576,165,353,382,2,122,391,8751,167,34,290,594,65,359,566,56,500,304,309,159,3742,292,329,34,3,563,131,398,5130,276,496,61,5046,43,1143,7690,44,415,106,565,542,60,1538,229,8539,309,222,373,10000,7,1528,264,128,225,515,74,328,554,364,198,1980,39,5,10000,262,616,214,10000,491,10000,202,444,7435,566,356,
|10000,1,27,501,191,579,165,360,386,2,123,391,8761,168,34,294,595,65,363,576,56,510,304,310,161,3807,295,329,34,3,564,132,400,5237,278,504,61,5112,43,1158,7711,44,417,107,572,545,60,1540,233,7967,310,222,378,10000,7,1528,267,129,225,521,74,330,562,370,199,2012,39,5,10000,263,622,217,10000,493,10000,205,450,7474,576,358,
|10000,1,27,507,194,585,166,364,390,2,123,393,8905,170,34,295,595,65,369,578,56,514,306,316,162,3883,298,330,34,3,564,133,405,5312,283,513,61,5158,43,1170,7869,44,424,107,572,552,60,1569,236,8119,315,223,381,10000,7,1529,270,129,225,527,74,335,571,373,202,2055,39,5,10000,264,633,219,10000,499,10000,205,450,7544,586,362,
|10000,1,27,513,194,591,167,370,391,2,123,400,9072,171,34,295,605,65,371,581,56,514,306,322,163,3914,298,336,34,3,565,134,412,5417,283,521,61,5187,43,1179,8015,44,427,107,582,555,60,1603,236,8228,320,223,383,10000,7,1538,272,130,227,537,74,341,571,376,202,2068,39,5,10000,266,641,222,10000,501,10000,205,452,7571,589,369,
|10000,1,27,514,194,591,169,376,392,2,123,401,9107,173,34,296,606,65,378,591,56,519,307,323,164,3941,303,337,34,3,575,135,418,5438,287,527,61,5283,43,1181,8170,44,434,108,591,555,60,1635,238,8230,326,225,387,10000,7,1555,274,130,230,538,74,343,571,380,204,2112,39,5,10000,271,654,222,10000,502,10000,206,452,7671,590,373,
|10000,1,27,515,196,591,171,380,397,2,123,407,9224,173,34,297,608,65,383,595,56,526,311,327,166,3956,306,340,34,3,584,136,423,5541,290,532,61,5379,43,1194,8250,44,435,108,603,565,60,1646,241,8243,327,227,388,10000,7,1589,277,131,232,549,74,343,574,380,204,2118,39,5,10000,276,657,222,10000,508,10000,207,456,7704,602,376,
|10000,1,27,520,199,598,173,387,397,2,123,411,9365,173,34,301,615,65,387,605,56,526,313,333,167,3980,307,344,34,3,587,138,426,5562,292,532,61,5381,43,1207,8385,44,440,109,605,574,60,1679,245,8265,329,230,395,10000,7,1603,282,132,234,559,74,343,579,385,207,2127,39,5,10000,279,657,223,10000,518,10000,208,461,7771,607,379,
|10000,1,27,526,201,601,175,388,398,2,123,412,9534,175,34,301,627,65,392,613,56,527,318,335,169,4050,307,349,34,3,591,140,431,5654,294,535,61,5503,43,1228,8504,44,445,109,617,586,60,1681,246,8271,335,230,399,10000,7,1613,287,133,234,559,74,346,586,389,208,2142,39,5,10000,281,664,227,10000,519,10000,208,463,7851,608,385,
|10000,1,27,527,204,609,178,388,399,2,124,413,9581,175,34,305,636,65,393,616,56,538,324,337,171,4062,307,356,34,3,595,141,432,5754,297,541,61,5581,43,1235,8571,44,451,109,629,595,60,1718,249,8359,338,234,399,10000,7,1641,292,135,236,565,74,349,587,393,209,2158,39,5,10000,284,671,229,10000,528,10000,208,469,7939,618,387,
|10000,1,27,528,206,611,181,393,406,2,125,417,9674,176,34,310,648,65,394,622,56,543,328,343,173,4133,310,357,34,3,607,143,440,5780,297,541,61,5664,43,1246,8699,44,459,109,634,596,60,1750,252,8496,342,235,404,10000,7,1671,297,135,238,573,74,349,588,394,209,2185,39,5,10000,287,674,229,10000,535,10000,211,474,8105,631,387,
|10000,1,27,536,206,618,183,395,407,2,125,425,9825,178,34,314,659,65,394,633,56,543,334,343,173,4220,313,361,34,3,609,143,441,5796,299,548,61,5689,43,1271,8781,44,460,109,639,599,60,1751,256,8647,345,238,404,10000,7,1682,297,136,242,583,74,353,590,394,209,2186,39,5,10000,291,676,232,10000,540,10000,214,477,8250,642,387,
|10000,1,27,539,206,629,184,403,415,2,64,431,9929,181,34,318,662,65,396,637,56,543,335,346,173,4279,313,367,34,3,613,144,448,5838,304,553,61,5765,43,1281,8911,44,464,109,647,606,60,1754,259,8795,347,239,411,10000,7,1699,298,138,245,585,74,355,593,396,209,2192,39,5,10000,295,679,235,10000,542,10000,216,485,8252,651,388,
|10000,1,27,549,209,642,187,411,421,2,64,438,9982,183,34,319,663,65,397,649,56,544,339,351,175,4307,315,367,34,3,625,144,448,5889,309,564,61,5884,43,1306,9091,44,464,109,659,609,60,1786,261,8867,351,243,413,10000,7,1716,302,140,247,585,74,355,597,400,209,2204,39,5,10000,297,692,238,10000,551,10000,217,487,8311,664,393,
|10000,1,27,553,212,652,187,419,423,2,64,441,10000,184,34,319,669,65,405,649,56,551,343,356,177,4315,316,369,34,3,628,145,452,5926,313,568,61,5942,43,1314,9265,44,473,109,669,621,60,1792,262,8971,357,243,421,10000,7,1728,306,140,247,588,74,362,598,400,210,2223,20,5,10000,301,705,242,10000,562,10000,220,496,8491,670,395,
|10000,1,27,564,214,662,187,425,423,2,64,444,10000,186,34,319,682,65,411,649,56,553,345,363,179,4368,164,373,34,3,633,146,461,1531,315,578,61,5974,43,1329,9293,44,475,110,671,628,60,1801,264,9175,359,243,421,10000,7,1764,309,142,250,588,74,369,602,404,212,2269,20,5,10000,303,715,244,10000,566,10000,223,498,8592,672,403,
|10000,1,27,573,217,665,187,428,426,2,64,448,10000,189,34,320,691,65,417,655,56,558,349,369,181,4450,165,379,34,3,641,148,465,1549,319,580,61,6078,43,1347,9430,44,475,110,672,635,60,1815,267,9298,359,243,428,10000,7,1784,314,143,254,600,74,369,606,412,215,2303,20,5,10000,308,721,247,10000,566,10000,226,508,8715,677,411,
|10000,1,27,581,220,668,187,435,431,2,64,455,10000,190,34,326,691,65,422,665,56,567,349,373,183,4515,167,386,34,3,648,150,469,1549,321,586,61,6080,43,1352,9530,44,480,111,679,637,60,1846,268,9506,366,247,81,10000,7,1808,320,143,256,603,74,370,617,413,216,2328,20,5,10000,314,727,250,10000,566,10000,226,514,8889,680,411,
|10000,1,27,592,220,671,189,435,431,2,64,460,10000,193,34,327,698,65,426,672,56,572,355,380,186,4534,168,386,34,3,649,151,474,1550,323,593,61,6190,43,1368,9688,44,488,111,692,647,60,1865,269,9536,373,249,81,10000,7,1845,325,143,257,615,74,374,622,414,219,2328,20,5,10000,320,728,254,10000,566,10000,229,521,9016,686,417,
|10000,1,27,603,222,676,189,443,438,2,64,461,10000,196,34,331,707,65,434,683,56,578,362,380,186,4608,169,387,34,3,654,151,475,1556,327,604,61,6221,43,1371,9748,44,495,111,692,650,60,1881,270,9645,373,250,81,10000,7,1882,329,143,261,619,74,381,622,419,222,2350,20,5,10000,322,743,257,10000,223,10000,232,527,9027,697,424,
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