数学的东西(BZOJ1951)

#include <cstdio>
#define LL long long 

  LL finmo=;
  LL fac[][],inv[][];
  LL tmp[],rev[];
  LL n,g,x,y;
  const LL mo[]={,,,};

  LL qpow(LL bas,LL pow,LL mo){
      LL ret=;
      for (;pow;bas*=bas,bas%=mo,pow=pow>>){
        if (pow&) ret*=bas,ret%=mo;
    }
    return(ret);
  }//快速幂

  LL C(LL t1,LL t2,LL mopo){
      if (t2>t1) return();
      return((fac[mopo][t1]*inv[mopo][t2])%mo[mopo]*inv[mopo][t1-t2]%mo[mopo]);
  }//组合数

  LL lucas(int t1,int t2,int mopo){
      LL ret=;
      while(t1||t2){
        ret*=C(t1%mo[mopo],t2%mo[mopo],mopo);ret%=mo[mopo];
      t1/=mo[mopo];t2/=mo[mopo];
    }
    return(ret);
  }//lucas定理

  LL solve(LL num){
      for (int i=;i<=;i++) tmp[i]=lucas(n,num,i);
    LL ret=;
    for (int i=;i<=;i++)
      ret+=tmp[i]*(finmo/mo[i])*rev[i],ret%=finmo-;
    return(ret);
  }//线性同余方程的解

  void exgcd(LL a,LL b,LL &x,LL &y){
      if (b==){
        x=1LL;y=0LL;return;
    }
    exgcd(b,a%b,x,y);
    LL t=x;x=y;y=t-(a/b)*y;
  }//扩展欧几里得

  int main(){
      scanf("%lld%lld",&n,&g);
      for (int i=;i<=;i++){
        fac[i][]=;inv[i][]=;
      for (int j=;j<mo[i];j++) {fac[i][j]=(fac[i][j-]*j)%mo[i];inv[i][j]=qpow(fac[i][j],mo[i]-,mo[i]);}
    }
    for (int i=;i<=;i++){
      exgcd(finmo/mo[i],mo[i],x,y);
      rev[i]=(x%mo[i]+mo[i])%mo[i];
    }

    LL ans=;
    for (int i=;i*i<=n;i++)
     if (n%i==){
      ans+=solve(i);ans%=finmo-;
      if (n/i!=i) ans+=solve(n/i),ans%=finmo-;
    }

    LL finans=qpow(g,ans,finmo);
    if (g==)printf("0\n");else printf("%lld\n",finans);
  }