N=100000;
M=2000000;
Q=0;
u=1;
v=2;
t=21;
A=[66589,48392,791767,104800,766778,53663,117659,914981,951118,653732,575320,338907,972492,787435,419335,686231,200298,484286,911160,319926,342098,13027,218118,551174,673663,135187,425876,7946,34710,16232,222780,564427,411158,220091,436842,594581,169169,767438,28152,192470,224546,321466,419666,708264,386909,777843,619576,980376,425437,644629,341669,425850,991725,621089,414369,230153,734350,386891,122217,33416,187842,402043,371724,20803,230992,169347,454823,92030,675552,962107,457259,187143,237686,78339,173403,296865,145633,533253,34915,553647,781018,457695,490350,35820,964828,205475,666319,790660,59293,522870,555159,304155,160228,63664,79580,1565,739026,322592,434591,649200,108979,432807,603983,644537,489249,190723,776729,898396,743587,265650,412281,21394,474618,763422,454999,196532,301360,329486,39440,199356,495178,187339,269224,542958,569616,689229,146335,532674,808468,736662,954323,372964,83856,894201,236426,135640,977278,578143,575099,515191,307433,267493,123213,754655,271562,869648,965155,198991,351121,312109,30109,919349,903619,841508,184318,840881,500317,47342,3712,687796,652251,228310,51632,607391,871969,564512,943916,826186,558038,214953,282228,747220,850596,491518,173888,595263,379429,65044,987544,797877,347778,41430,514314,818995,32994,804807,651252,822414,927634,760603,2963,974394,110817,657766,45448,200107,898237,352118,779444,319932,872019,670252,568358,921605,915704,554970,293401,395754,16505,496503,317238,284195,575596,449011,761949,10969,518441,89710,199609,870630,611093,338367,57314,984635,462636,388820,783901,560715,207965,923976,624357,329646,224217,42339,81667,605547,840965,118566,130375,289980,937407,646410,986503,963892,556025,291864,838486,779600,400353,821938,797004,416306,525996,695250,875569,193212,256132,898504,775402,405770,609273,480478,629951,134302,390426,645294,941132,542133,169007,605838,479441,389728,393185,953675,400088,868725,318313,793568,985282,945541,540350,948428,388984,711445,691119,665393,13399,257829,288273,452303,160098,696143,764266,915065,612034,483667,383626,416471,605446,141849,238040,422484,664435,504062,40156,349415,915044,12620,124662,711136,814845,636404,201075,788612,169644,25876,822515,546609,406094,587644,848235,300769,672883,403407,189045,975167,754674,203750,654822,85914,707853,662050,557925,375233,31255,810307,454157,531790,968888,588283,745069,41665,601299,154344,762649,95714,701338,870852,230976,140270,740394,354628,408197,968638,194656,747682,31451,7184,548891,978782,56050,401495,707049,414918,981138,741605,162990,51988,999484,691168,853134,65496,252252,542170,410117,528671,746965,287472,108391,644380,48520,393762,528498,519207,647659,414440,752327,959792,581100,758551,503539,375522,297565,834008,429991,949826,795288,40542,401306,796755,543992,7208,811589,793680,897711,629941,770442,386325,789161,953272,406123,729535,845191,524423,781935,447065,6033,487699,967545,774125,500101,122704,76869,176507,651597,806540,368143,611725,787317,31065,815021,171330,451977,962298,329476,662814,462145,641797,6996,595668,896863,543613,335662,524324,337039,706116,851956,580129,583013,822161,575202,100950,563803,748770,4218,595172,148957,147435,89211,690737,824640,297651,972284,163554,7260,703326,650605,412638,164284,995031,200190,619803,997225,264688,908095,119805,608379,480967,943805,608870,879318,267348,682680,188924,368779,146991,323643,895554,288357,214248,84660,791063,661429,793037,748200,870280,158173,745448,358503,349097,660885,252941,798693,651876,513838,723714,186443,432485,276957,438805,343196,715964,221119,781793,123173,787371,496663,933727,704942,903661,261554,608842,214215,878040,618062,842448,353364,889025,188536,202787,339424,471182,619406,832821,174931,187757,439393,94111,572115,261401,459854,413772,320909,460809,854121,182248,420029,824392,576797,67950,996691,562974,179830,915251,710090,621403,995749,398621,312452,769604,787430,849748,436147,825587,112569,71488,328844,869327,391196,793616,675167,329350,742051,28466,870642,934904,359514,135230,957711,304329,643779,717290,58169,440253,720676,735337,884972,537758,406885,786782,836060,273377,140371,281952,600462,962569,877603,579948,953413,678187,135454,283436,284437,180349,565412,792243,230404,660648,275016,523028,226795,381766,133235,548701,705186,285266,736124,426654,226094,680038,87144,251685,766524,592604,326764,565823,642379,377555,468727,695020,403233,321751,939045,368734,816268,759446,255668,878968,784218,956021,149053,238637,60478,579545,528499,503328,121806,84967,936432,109565,597414,597615,356904,859308,898475,196627,305643,296984,254437,880055,688705,833995,371289,555142,79550,576254,59495,577888,415631,246729,704556,861921,486575,839563,306892,340036,458909,766628,123839,428178,334577,623123,387859,668208,68641,113653,913303,861744,219052,217071,473130,965493,58990,625710,791980,954703,403651,998946,138446,131991,242853,426947,309902,338774,868774,576354,25713,412563,24600,20494,121832,977068,187855,87691,73957,116402,991468,788680,313621,798043,157099,505743,283015,184128,24794,162669,844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