BZOJ3501 : PA2008 Cliquers Strike Back

#include<cstdio>
typedef long long ll;
const int N=7284,P=999999598;
ll n,m;int a[4]={2,13,5281,7283},f[N]={1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,190899322,382958947,480146167,864902768,77080323,744549521,179028420,7054491,550147557,604197592,570342585,944062145,387879224,401449617,770869529,183414916,4280247,316746725,653486782,180319907,335856599,70468498,855407155,983433965,231403320,149249947,648913159,340460910,764716907,977561149,326938348,99934771,159695771,626278792,62670713,132653247,59357674,527142103,661211915,149126128,333857527,661708683,347209904,142574663,984776691,235283292,339165187,737258613,921812370,298840587,714855343,785747412,578156629,850854071,611687532,883228189,646494861,812747584,801181323,354062485,734584914,588941721,569513841,723841432,458361117,398864661,539856762,30592783,598895321,926051332,667372881,402414575,926090628,722615155,320574843,532450284,483632183,239195859,264476384,924799697,754893475,248176184,849558909,698584429,351966250,859990297,326608249,888694306,182458039,449189209,316228194,712827043,557174983,137060034,74870913,89997181,326766670,293149645,752267857,829957972,33192877,894072489,879345308,483869167,294614041,229279162,147355423,663762555,434644220,577891423,395447259,166001994,815927023,439369581,923609006,756121781,375132429,440527804,467644699,917110397,341694806,8099431,759390805,187880772,752619443,321726629,35081380,211716005,943383293,392628286,693149851,346004097,833807682,77926225,58368823,54044814,377428017,843016025,182906320,604981549,411523231,525819950,697374615,129688937,159913614,719670399,248834085,146155566,781605887,828105927,719951836,364560029,750133363,108278620,476287313,89655075,615662194,18816105,714687271,971074576,702005273,962271943,268436914,752732391,417318051,45649006,821761931,275655885,626310536,661558521,8050817,707181348,751265371,714138091,594617414,221647491,89830795,459417056,211520221,363595259,401284460,448154441,251405045,30777758,651569713,469482107,879962712,759397211,99257069,479670226,685537083,199771043,181375564,366575065,530619845,366720490,64477569,711148287,469133244,758124789,516385353,696751534,905517047,762290647,60670126,876014261,31950283,472741914,266114855,66511619,428323194,686405513,606618697,107645162,986590869,197599097,167363454,902480321,874475959,98575902,567528183,211143515,201102868,304427839,654963761,717678582,663392293,672583793,849521470,731542383,615877777,740908378,75957645,3910243,900214474,210924005,978314777,963608796,211029509,537904487,64855820,620515485,940326291,700070524,405448913,267978707,471833338,21731927,895617857,244285488,481615455,160672985,430869120,88829931,840307039,406184472,10392469,245517423,846557476,999479791,210088281,339725044,797121443,847375829,389551472,906317829,759468939,890227694,492710583,457082513,727917430,623422549,909579929,717039618,752522365,531435595,721105488,944893689,320279293,354704896,165277287,697896113,542521886,72244681,315361365,375651062,901486891,141381629,479208458,880566659,252763831,705451262,850703119,715858791,898350026,755113319,736185875,557429614,112277789,399985539,516739288,797693805,855693195,706894478,368216617,351741433,571675104,373389745,106539441,156009864,641957681,689283145,73513198,423856783,479848439,907273286,723297789,64519773,565096458,150684223,793006457,184645700,410301175,702511595,854174864,25297341,953436865,692328600,618990271,916323355,31185424,981914783,661239901,443987948,499503085,689810879,345507464,114387339,688902911,99819960,123944631,981151147,460242194,953417103,158853749,674234416,708099149,746363547,284374864,721732561,267931725,841141692,450534953,808475155,736344724,940364839,433029211,985001732,930134051,109646561,45813730,350287793,831264031,482658654,34918779,270985941,433036102,882964507,18385135,797584428,637553685,100248421,801893832,494551433,335012585,635358942,683239163,363317309,184836688,537814577,845553707,303500450,721013689,600441285,753782314,492819377,931297793,133381828,734889369,113341345,457163422,780138123,109791993,405672466,914083663,317129587,597850254,451370891,378762145,875356916,717574859,139483727,57894786,401175865,979052513,979443988,371634669,840745523,289880938,223427683,609525805,303686240,47083861,69134553,845731192,129340081,98017409,465780484,439408677,808928897,828013748,146530781,409143751,76293482,527225263,936259389,120822456,267846781,133115199,250046624,828233269,907151365,408801718,381317375,938624801,250935810,611195713,383694317,509855672,354246589,578989479,889853034,540792995,75407003,455579738,627925997,185099389,511281100,21817607,566062683,747390404,368634951,991117593,309533544,986565431,931749921,518117950,354006809,262617021,956167822,335978355,823521423,274513718,267259593,825331319,787679782,999223929,303716769,973268748,780116557,13293453,72939584,528943633,527910313,862242194,107930421,380412705,530999560,257772185,227069603,936449126,906870649,520652941,956908310,531386427,754086221,637777624,451461305,49830987,625854382,653421933,428811489,867608348,477201853,302209335,116724436,583108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int cal(int x,ll n){
  int i,j,k,m=0,b[N],c[N],d[70];
  for(i=0;i<=x;i++)b[i]=f[i]%x;
  while(n)d[m++]=n%x,n/=x;
  for(i=1;i<m;i++)for(j=1;j<=d[i];j++){
    for(k=0;k<x;k++)c[k]=(b[k]*i+b[k+1])%x;
    c[x]=(c[0]+c[1])%x;
    for(k=0;k<=x;k++)b[k]=c[k];
  }
  return c[d[0]];
}
ll pow(ll a,ll b,ll p){ll t=1;for(a%=p;b;b>>=1LL,a=a*a%p)if(b&1LL)t=t*a%p;return t;}
ll bell(ll n){
  if(n<N)return f[n];
  ll t=0;
  for(int i=0;i<4;i++)t=(t+(P/a[i])*pow(P/a[i],a[i]-2,a[i])%P*cal(a[i],n)%P)%P;
  return t;
}
int main(){
  scanf("%lld%lld",&n,&m);
  printf("%lld",pow(m,bell(n),P+1));
  return 0;
}