N=100000;
M=100000;
Q=0;
u=1;
v=2;
t=2;
A=[959613,194150,85516,394977,870052,300505,900903,647300,231641,734416,481762,684211,758915,137869,352605,391761,479479,66137,556643,350877,43736,161855,751745,712737,997176,784526,211646,408521,24991,685052,44735,26566,542249,350565,510457,425603,884803,307583,328155,120818,644865,333315,114972,249303,47403,327479,583903,808328,848801,323201,329666,692330,551181,226645,901688,844716,197417,490643,113176,840761,57370,11473,83113,227769,286476,309857,313489,416058,672166,257200,167546,16653,341274,637326,200920,78684,407043,214905,728596,25845,188335,747691,958318,119139,902569,757574,992470,154386,467847,748363,215379,338474,988362,234968,228538,109686,420102,411687,574519,742229,952600,613404,218114,839313,538207,300423,166595,932326,942375,323494,974033,414403,358754,188179,414615,709820,973951,760372,77025,589633,246932,75235,907124,397028,657903,453335,268453,263536,695911,170258,610640,378975,304784,759773,104349,78366,923798,965877,490923,428418,130430,453673,583808,782120,852467,438414,269549,882612,367192,255712,62279,499372,472473,72179,818698,720440,180120,330575,461100,422316,823211,892465,468991,286218,222697,517909,209324,11841,493133,546912,988322,2143,944678,745593,194005,758336,336432,704523,462371,40815,439844,574111,162111,415524,258150,873547,948647,804077,810916,639700,145191,658746,398069,351761,824218,887550,91304,563408,190298,804522,707865,621261,944002,45213,154167,674894,652251,891917,492544,72268,304820,310653,761003,736240,472930,238274,286744,14720,317581,191009,923664,110250,60465,450805,480227,694092,398674,369374,84027,166604,879078,351236,238295,167686,653881,770560,57154,381727,529094,71454,699973,838960,287414,997121,980238,7079,825417,364239,186205,78786,442548,504782,807035,358521,739351,871213,990536,594610,93489,253585,808084,229574,932921,718467,64575,537440,921671,565661,612169,860232,412911,553798,479668,966412,495413,423048,601110,921571,250445,985621,573779,893145,435333,769967,801637,270767,954355,171465,87038,199260,404532,401803,53699,281903,928614,541792,436813,902995,302539,63646,117467,279096,907021,519555,178031,492682,94546,988843,112242,263195,352216,83071,369431,332897,170538,226912,455389,171267,44189,391515,267499,734462,265701,595172,103305,707168,70452,953229,496104,356354,855216,9547,276562,344674,599798,225576,542493,87569,429325,790851,470159,599658,355316,556777,737446,900660,986433,93903,331149,756792,201560,490842,14745,860429,366580,436061,681591,359740,675975,555588,525323,362010,814313,485225,453244,192884,386578,366737,400956,307632,990266,101303,904234,422425,410982,95371,83519,537071,239116,833539,787355,318852,279447,866951,600060,478795,447352,964865,428542,623196,143189,772905,406318,946429,752829,754211,540510,817869,498185,879333,792869,563418,505074,338438,983564,558452,554317,858289,506399,452728,883664,988890,386864,101256,762572,705802,732753,768274,197602,75968,291097,286370,789633,850438,907694,639639,36449,379866,836614,651794,669006,38043,838153,185002,756284,872789,226644,239954,579005,793414,250836,74000,853084,216269,904079,70729,471147,80116,424856,728802,518459,291268,880707,959323,338100,343292,458335,274391,625600,852206,110604,651802,874847,38415,24987,809416,861924,604094,592896,326654,326435,607218,284506,644254,167987,25980,967392,281595,371395,208621,612161,116004,230578,406846,917829,237173,814112,723208,86098,249644,334697,865662,335951,443774,266060,764807,926259,766735,889421,388620,115084,244482,590293,247585,209716,104127,826922,913390,836937,733348,320529,229574,405004,28120,910304,269384,528178,503499,421961,187738,380811,657400,222471,713641,763204,276870,883988,803084,62912,726756,22338,965160,621554,145179,179198,808413,833192,956236,784958,549747,141108,637027,799039,263400,447160,545562,378292,740500,658697,514367,191400,306926,917368,27684,621840,188878,274653,356777,911749,4837,328390,986790,944908,58905,860180,742462,438103,76642,527866,302162,526376,236703,687076,543393,853619,740371,9910,409015,470136,634106,661583,751658,873762,472038,577614,321430,7496,650318,471277,579331,584399,470203,923085,249399,450369,408651,976968,349015,591594,627670,198769,450809,34785,451796,972161,955503,293777,327949,868101,958141,714474,454268,290062,938672,239543,59403,611657,842183,745126,792392,202597,631719,858578,762986,448417,487108,29240,870663,11809,229824,50156,26186,543620,310047,378500,110586,420337,872851,582173,358104,968228,707143,12434,339683,863566,751002,460275,719539,226129,875658,795154,974042,427147,248830,742858,464820,203086,694501,993263,669464,143478,179076,589646,847587,401911,608973,895791,529665,302443,732956,301831,308814,19601,736432,151906,892722,135320,718234,145510,244739,930389,433385,70302,922470,410412,311567,873323,464297,47762,136116,573704,558785,119849,202505,777264,813278,985631,996207,942756,73324,652133,892868,240197,799836,618290,370730,709234,861761,684006,289481,207528,577538,281495,27561,724711,770134,921442,106087,805583,277514,697108,255272,790287,248882,411714,90481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