T=100;
N=80;
M=800;
P=[|219,354,6931,64,595,521,718,587,404,5044,790,311,557,383,43,484,401,620,6099,83,8921,1022,727,173,544,31,390,7562,5,347,97,747,109,8275,669,3329,382,235,724,8051,165,636,4661,508,720,643,639,635,85,272,89,481,9002,88,8814,791,395,5555,89,165,695,126,733,603,7442,1786,288,492,37,300,1483,398,26,8443,747,188,448,245,691,3381,
|220,355,6994,64,603,531,721,596,410,5076,807,315,561,389,43,494,401,623,6201,83,8949,1036,727,174,546,31,391,7689,5,351,98,752,109,8357,677,3388,389,238,734,8108,166,648,4674,516,734,647,640,641,85,274,90,483,9198,88,8993,807,398,5572,90,166,695,127,745,609,7541,1825,292,495,37,304,1378,406,26,8571,762,190,451,249,695,3418,
|221,359,7051,64,604,533,735,605,415,5116,819,318,570,389,43,502,406,625,6337,83,9023,1049,735,174,553,31,396,7822,5,358,98,766,109,8410,686,3435,391,238,740,8170,168,658,4776,523,744,650,650,649,85,275,90,486,9407,89,9198,814,406,5670,91,168,702,127,745,619,7594,1839,297,499,37,309,1379,407,26,8620,771,190,460,253,697,3477,
|225,362,7109,64,610,543,742,607,421,5231,819,324,574,391,43,503,411,635,6378,83,9070,1066,740,177,561,31,401,7913,5,362,98,776,110,8585,694,3475,397,239,745,8176,170,663,4790,529,744,663,655,655,85,278,91,491,9442,90,9284,829,406,5780,92,170,708,128,760,620,7733,1867,298,504,37,315,1380,414,26,8734,773,192,464,257,704,3541,
|225,366,7125,64,622,547,743,610,428,5256,825,328,575,396,43,324,418,640,6402,83,9157,1078,745,177,563,31,405,7952,5,363,98,792,110,8620,698,3512,404,241,756,8318,170,674,4889,540,748,674,667,666,85,281,92,496,9482,90,9338,842,407,5906,93,172,718,128,769,621,529,1892,299,513,37,316,1385,415,26,8763,773,193,469,257,716,3564,
|229,366,7265,64,628,553,752,617,436,5302,838,332,586,399,43,326,425,647,6485,83,9262,1090,745,180,563,31,411,8085,1,370,99,795,29,8629,710,3521,406,241,758,8357,171,683,4981,547,755,677,669,667,85,282,92,498,9491,90,9369,847,409,6027,93,174,729,128,774,629,529,1914,299,516,37,322,1387,422,26,8867,781,196,472,257,718,3632,
|229,366,7406,64,635,559,766,628,438,5359,850,333,598,403,43,327,433,647,6592,83,9342,1107,746,180,563,31,416,8178,1,376,99,806,29,8699,718,3582,409,241,761,8361,173,697,5034,551,768,689,670,672,85,282,93,505,9532,91,9558,863,411,6083,94,176,729,129,789,638,332,1941,302,519,37,324,1394,427,26,8944,794,198,480,260,720,3654,
|229,368,7505,64,639,569,781,640,443,5367,856,335,598,410,43,327,441,655,6682,83,9403,1122,755,183,573,31,420,8364,1,383,100,812,29,8779,726,3618,409,241,771,8495,174,709,5077,560,769,689,683,676,85,282,94,513,9685,92,9655,872,415,6171,95,176,731,130,804,644,338,1962,307,528,37,327,1417,433,26,8961,802,199,484,262,724,3665,
|233,368,7661,64,651,578,789,644,448,5424,863,337,598,411,43,328,446,655,6787,83,9499,1139,764,184,575,31,427,8406,1,383,101,816,29,8865,730,3694,415,241,774,8557,177,715,5169,567,782,701,693,678,85,287,94,522,9781,92,9752,236,416,6255,96,178,739,130,816,656,340,2000,311,528,37,329,1446,439,26,9129,808,202,492,267,739,3716,
|234,368,7699,64,661,583,806,657,449,5538,880,343,602,417,43,329,447,659,6830,83,9600,1146,778,184,577,31,428,8591,1,386,101,818,29,8915,733,3750,420,245,779,8585,180,730,5218,568,797,704,693,690,85,288,94,533,9949,92,9852,237,417,6380,97,178,750,130,826,664,346,2043,317,538,37,331,1469,447,26,9136,812,204,497,272,750,3784,
|237,372,7731,64,675,584,820,667,457,5570,881,343,606,420,43,331,453,666,6857,83,9759,1146,783,186,577,31,436,8713,1,392,101,818,29,8952,746,3802,421,245,779,8753,183,745,5220,570,804,712,706,691,85,288,95,537,9995,92,9897,237,417,6454,97,180,760,131,842,673,347,2086,323,549,37,336,1486,455,26,9272,815,205,499,276,759,3828,
|241,375,7765,64,675,593,824,672,460,5604,896,343,607,427,43,333,462,670,6879,51,9875,1147,793,187,579,31,437,8836,1,396,101,830,29,9014,756,3883,425,248,787,8797,184,753,5292,575,821,719,712,703,85,292,96,538,10000,92,9963,237,425,6497,97,180,766,133,855,680,348,2115,324,557,37,336,1516,463,9,9365,821,183,500,278,773,3860,
|245,379,7936,64,686,594,837,673,467,5637,908,347,618,428,43,339,467,678,6882,51,10000,1168,802,190,583,31,437,8993,1,398,102,831,29,9134,765,3967,429,250,797,8912,186,766,5376,583,837,725,727,714,85,297,61,543,10000,2,9991,241,425,6615,97,182,766,135,873,687,351,2127,325,563,37,342,1536,465,9,9381,826,186,505,280,777,3933,
|249,380,8067,64,689,598,853,673,469,5750,921,353,628,435,43,339,472,685,6904,51,10000,1168,802,192,588,31,438,9005,1,406,103,839,29,9199,779,3971,429,252,802,8966,187,781,5376,591,852,740,736,726,85,301,61,553,10000,2,10000,245,432,6661,97,182,773,135,884,693,352,2151,327,567,37,344,1569,469,9,9438,831,188,508,282,780,3952,
|253,381,8125,64,695,605,866,681,478,5789,923,355,638,443,43,341,477,692,6920,51,10000,1174,802,192,589,31,438,9195,1,412,103,856,29,9284,786,4033,429,253,818,9072,189,792,5444,598,868,752,749,729,85,302,61,564,10000,2,10000,245,437,6758,98,184,773,136,895,694,358,2158,329,579,37,348,1570,469,9,9517,840,189,514,285,787,3990,
|253,385,8176,64,705,605,866,685,481,5816,935,361,640,448,43,343,484,704,7035,51,10000,1179,804,192,596,31,444,9354,1,416,104,864,29,9461,789,4057,434,253,832,9089,192,792,5469,608,884,756,749,737,85,305,61,568,10000,2,10000,245,437,6837,98,185,781,138,900,701,359,2193,334,584,37,349,1600,475,2,9626,855,189,515,286,803,4071,
|257,387,8315,64,706,610,882,694,490,5878,949,367,647,451,43,349,493,713,7132,51,10000,1195,810,194,596,31,444,9396,1,424,104,868,29,9602,796,4059,440,253,839,9189,194,803,5559,611,887,772,754,740,85,309,61,580,10000,2,10000,245,438,6869,98,188,782,138,916,702,362,2225,334,584,37,352,1604,479,2,9705,870,192,517,289,810,4089,
|257,390,8442,64,720,611,884,698,490,5942,967,369,647,457,43,355,501,719,7265,51,10000,1205,823,196,605,31,445,9519,1,426,104,874,29,9720,805,4079,443,255,855,9301,197,811,5600,614,890,776,755,516,85,313,61,592,10000,2,10000,246,439,6902,98,190,790,140,930,707,365,2225,334,596,37,353,1632,482,2,9806,888,195,522,294,810,4093,
|26,397,8620,64,723,613,891,705,492,1947,981,371,649,457,43,362,503,675,7359,51,10000,1205,838,199,606,31,449,9675,1,426,104,887,29,9740,817,4115,450,258,872,9426,200,824,5600,627,909,782,758,520,85,314,61,601,10000,2,10000,250,444,6932,98,190,803,141,931,714,367,2249,336,603,37,358,1659,492,2,9897,906,197,532,297,811,4101,
|26,405,8642,64,732,616,899,717,496,1948,999,377,652,459,43,369,510,680,7510,51,10000,1229,854,199,607,31,449,9832,1,426,105,906,29,9796,823,4134,451,262,886,9586,201,835,5699,638,925,795,773,526,85,316,61,606,10000,2,10000,254,444,7028,99,193,809,142,937,729,367,2292,338,608,37,364,1670,492,2,9930,911,198,534,298,812,4154,
|26,412,8783,64,739,626,899,720,497,1973,1001,384,660,467,43,373,511,682,7548,51,10000,1230,871,201,614,31,449,10000,1,429,105,918,29,9835,839,4137,451,262,892,9615,204,838,5749,639,943,803,776,526,85,321,61,611,10000,2,10000,256,449,7032,99,194,818,143,954,734,371,2310,340,615,37,367,1697,495,2,10000,911,199,536,303,817,4171,
|26,419,8863,64,745,635,904,725,497,2010,1002,387,660,475,43,373,518,682,7573,51,10000,1253,871,203,614,31,457,10000,1,431,105,933,29,9962,851,4194,451,266,904,9657,206,852,5816,648,957,810,778,528,85,324,61,620,10000,2,10000,260,457,7171,99,194,820,143,958,735,377,2332,344,620,37,373,1726,500,2,10000,930,199,543,305,823,4249,
|26,422,9004,64,750,639,911,733,504,2054,1003,390,665,481,43,375,522,688,7745,51,10000,1270,886,203,625,31,460,10000,1,432,105,939,29,10000,865,4288,459,270,911,9665,206,860,5933,651,958,818,793,533,85,328,61,632,10000,2,10000,263,458,7206,99,197,822,144,970,746,377,2365,345,629,37,379,1747,502,2,10000,934,199,552,308,824,4312,
|26,424,9115,64,765,645,914,738,504,2060,1012,390,678,486,43,377,533,691,7810,51,10000,1295,889,203,633,31,468,10000,1,434,105,955,29,10000,876,4293,464,271,911,9813,207,874,6062,656,958,831,800,539,85,331,61,642,10000,2,10000,43,467,7321,100,199,839,146,976,750,384,2406,350,632,37,382,1755,510,2,10000,943,199,559,310,826,4330,
|26,431,9151,64,776,657,924,743,508,2098,1017,390,685,495,43,377,539,698,7960,51,10000,1301,894,206,633,31,472,10000,1,439,106,962,29,10000,891,4293,466,273,921,9881,208,890,6112,667,968,835,808,549,85,331,61,653,10000,2,10000,43,469,7323,100,200,851,146,980,756,390,2423,350,634,37,387,1770,510,2,10000,951,202,560,310,832,4352,
|26,434,9183,64,792,663,927,757,514,2125,1018,395,692,498,43,381,550,709,8078,51,10000,1304,903,209,646,31,476,10000,1,448,107,969,29,10000,910,4351,472,274,936,9885,210,904,6170,671,977,837,819,557,85,332,61,664,10000,2,10000,43,478,7431,100,200,862,146,981,760,392,2466,355,642,37,391,1798,512,2,10000,955,205,560,316,833,4382,
|26,439,9230,64,793,668,936,771,518,2161,1018,396,700,505,43,387,552,721,8125,51,10000,1319,909,210,646,31,481,10000,1,454,108,983,29,10000,924,4396,476,277,949,10000,213,915,6224,683,987,844,829,560,85,334,61,675,10000,2,10000,43,485,7500,100,203,880,147,991,153,394,2478,360,643,37,391,1808,516,2,10000,960,208,568,321,836,4437,
|5,440,9432,64,798,681,946,786,522,2161,1025,397,715,507,43,393,560,736,8132,51,10000,1330,917,212,654,31,489,10000,1,460,109,992,29,10000,928,4461,485,280,949,10000,215,917,6344,690,1008,855,837,561,85,340,61,680,10000,2,10000,43,485,7657,100,205,881,148,993,155,395,2496,361,656,37,392,1842,516,2,10000,975,211,580,323,836,4483,
|5,449,9624,64,806,689,966,786,531,2182,1039,405,717,507,43,394,565,750,8227,51,10000,1338,927,213,665,31,489,10000,1,462,110,1010,29,10000,947,4464,490,284,963,10000,215,917,6451,702,1030,862,853,570,85,340,61,686,10000,2,10000,43,491,7717,101,206,884,148,1009,156,399,2500,361,659,37,392,1858,523,2,10000,979,214,590,325,850,1020,
|5,452,9791,64,822,695,976,802,534,2203,1048,413,727,514,43,394,569,751,8336,51,10000,1364,930,214,665,31,493,10000,1,462,111,1015,29,10000,963,4516,490,285,984,10000,215,917,6581,714,1051,876,860,577,85,344,61,697,10000,2,10000,43,491,7806,101,206,885,150,1018,156,399,2533,364,667,37,393,1881,531,2,10000,984,217,594,325,850,1031,
|5,456,9948,64,830,704,979,813,545,2236,1051,416,742,517,43,400,571,758,8375,51,10000,1374,936,214,670,31,499,10000,1,463,111,1020,29,10000,981,4524,495,289,990,10000,217,918,6590,721,1061,883,864,584,85,345,61,711,10000,2,10000,43,496,7849,101,206,888,152,1030,158,407,2587,366,681,37,397,1909,542,1,10000,1004,220,596,327,854,1051,
|5,456,10000,64,832,717,989,818,551,2263,1071,416,744,525,43,407,574,768,8438,51,10000,1385,946,215,673,31,507,10000,1,466,111,1033,29,10000,986,4558,497,289,995,10000,68,936,6703,726,1062,898,869,592,85,347,61,719,10000,2,10000,43,503,7885,101,209,899,154,1032,158,408,2600,369,692,37,402,1909,542,1,10000,1013,224,596,327,858,1060,
|5,461,10000,64,839,717,995,831,562,2289,1075,423,750,525,43,411,574,778,8516,51,10000,1415,966,189,679,31,509,10000,1,474,111,1043,29,10000,992,4653,500,292,1011,10000,68,942,6734,726,1068,905,886,596,85,349,61,509,10000,2,10000,43,510,8055,102,211,905,156,1054,160,408,2624,370,693,37,409,1909,553,1,10000,1024,226,606,328,871,622,
|5,468,10000,64,839,726,1011,833,573,2318,1079,424,753,535,43,416,584,778,8601,51,10000,1445,981,189,686,31,517,10000,1,476,112,1063,29,10000,1011,4693,509,295,1015,10000,68,959,6819,740,1091,906,895,606,85,353,61,515,10000,2,10000,43,519,8095,102,213,916,156,1076,162,411,2677,372,706,37,409,1916,554,1,10000,1042,227,606,333,873,630,
|5,470,10000,64,855,740,1020,838,579,2333,1099,425,763,544,43,417,593,783,8715,51,10000,1460,996,192,693,31,521,10000,1,481,113,1086,29,10000,1022,4766,514,299,1034,10000,68,980,6942,750,1096,918,903,612,85,358,61,521,10000,2,10000,43,526,8268,102,214,935,157,1085,164,417,2697,379,718,37,411,1934,558,1,10000,1052,230,617,334,883,630,
|5,473,10000,64,859,753,1030,839,590,2334,1110,426,765,545,43,423,595,795,8874,51,10000,1473,1008,192,693,31,526,10000,1,488,113,1089,29,10000,1040,4857,515,301,1040,10000,68,985,6980,760,1112,926,908,615,85,359,61,522,8493,2,10000,43,532,8295,103,215,940,159,1107,164,424,2727,386,721,37,413,1972,563,1,10000,1072,230,617,338,890,630,
|5,479,10000,64,867,754,1031,857,591,2359,1129,433,779,552,43,424,600,802,8906,51,10000,1485,1013,195,696,31,531,10000,1,489,114,1113,29,10000,1044,4942,516,306,1059,10000,68,988,7059,771,1123,938,919,625,85,366,61,532,8678,2,10000,43,538,8304,103,216,953,159,1118,166,429,2744,389,724,37,416,2004,572,1,10000,1084,232,623,341,904,640,
|5,489,10000,64,885,766,1047,875,593,2364,1144,439,787,561,43,425,604,813,8938,51,10000,1512,1032,196,708,31,541,10000,1,494,115,1117,29,1591,1064,5009,526,312,1064,10000,68,1008,7184,772,1126,956,921,635,85,367,61,533,8770,2,10000,43,542,8400,104,216,966,161,1141,166,434,2754,391,726,37,421,2033,575,1,10000,1087,233,634,343,922,646,
|5,491,10000,64,891,776,1058,878,598,2404,1151,448,804,562,43,429,609,817,8998,51,10000,1532,1041,196,714,31,500,10000,1,497,115,1122,29,1611,1074,5073,531,313,1081,10000,68,1015,7242,772,1135,963,929,635,85,373,61,544,8775,2,10000,43,550,8534,104,216,980,161,1149,168,440,2786,396,735,37,423,2062,584,1,10000,1089,234,638,349,924,658,
|5,497,10000,64,894,783,1079,879,599,2417,1168,449,804,567,43,432,622,821,9050,51,10000,1558,1061,197,716,31,503,10000,1,505,115,1123,29,1611,1094,5079,535,317,1100,10000,68,1030,7280,776,1156,980,944,648,85,379,61,550,8906,2,10000,43,557,8690,104,216,986,163,1164,169,446,2847,398,735,37,431,2082,591,1,10000,1113,236,649,351,943,663,
|5,504,10000,64,899,786,1098,889,607,2427,1170,453,815,576,43,432,624,827,9085,51,10000,1582,1070,197,725,31,511,10000,1,514,115,1137,29,1635,1114,5178,536,322,1110,10000,68,1041,7401,783,1167,988,951,655,85,380,61,558,9043,2,10000,43,558,8797,104,216,1006,163,1182,170,447,2881,401,750,37,434,2082,603,1,10000,1117,237,653,354,957,676,
|5,509,10000,64,910,795,1107,905,617,2445,1186,455,827,588,43,434,632,835,9271,51,10000,1603,1071,199,728,31,516,10000,1,522,115,1142,29,1661,1129,5267,545,326,1111,10000,68,1059,7560,789,1184,990,961,664,85,387,61,569,9190,2,10000,43,559,8816,104,216,1012,164,1192,171,450,2915,408,750,37,440,2103,608,1,10000,1141,239,655,359,978,678,
|5,516,10000,64,920,812,1129,914,627,2459,1195,456,831,595,43,440,635,837,9340,51,10000,1636,1094,200,735,31,521,10000,1,528,116,1163,23,1666,1152,5271,548,328,1119,10000,68,1073,7698,806,1186,998,974,676,85,387,61,570,9303,2,10000,43,559,8941,105,216,1015,164,1201,173,451,2922,414,753,16,440,2137,613,1,10000,1141,241,667,359,983,691,
|5,521,10000,64,930,828,1152,929,638,2474,1205,465,837,597,43,444,643,845,9512,51,10000,1655,1113,203,749,31,529,10000,1,532,116,1182,23,1703,1163,5318,557,333,1122,10000,68,1073,7728,816,1196,1004,990,677,39,391,61,574,9305,2,10000,43,568,9039,106,216,1035,165,1211,173,459,2988,419,764,16,449,2162,618,1,10000,1142,241,670,363,988,695,
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