BZOJ 1951: [Sdoi2010]古代猪文 ExCRT+欧拉定理+Lucas

欧拉定理不要忘记！！

#include <bits/stdc++.h>   
#define N 100000 
#define ll long long        
#define ull unsigned long long 
#define setIO(s) freopen(s".in","r",stdin) 
using namespace std;       
int array[10]={2,3,4679,35617};       
ll mult(ll x,ll y,ll mod) 
{     
    ll tmp=(long double)x/mod*y;   
    return ((ull)x*y-tmp*mod+mod)%mod;  
}
ll qpow(ll base,ll k,ll mod) 
{
    ll tmp=1; 
    for(;k;k>>=1,base=mult(base,base,mod)) if(k&1) tmp=mult(tmp,base,mod);
    return tmp;    
}
struct Lucas 
{    
    int mod;    
    int fac[N];     
    ll inv(ll x) 
    {
        return qpow(fac[x],mod-2,mod);      
    }
    void init(int p) 
    { 
        mod=p;  
        fac[0]=1;   
        for(int i=1;i<=mod;++i) fac[i]=(ll)fac[i-1]*i%mod; // inv[i]=qpow(fac[i],mod-2,mod);      
    }
    ll C(int n,int m) 
    {
        if(m==0) return 1;    
        if(n<m)  return 0; 
        return (ll)(1ll*fac[n]*inv(m)%mod*inv(n-m)%mod)%mod;  
    }
    ll solve(int n,int m) 
    {
        if(m==0) return 1;                            
        return (solve(n/mod,m/mod)*C(n%mod,m%mod))%mod;   
    }
}comb;
struct CRT 
{  
    int n;  
    ll arr[N],brr[N]; 
    ll exgcd(ll a,ll b,ll &x,ll &y) 
    {
        if(!b) 
        {
            x=1,y=0; 
            return a; 
        }
        ll gcd=exgcd(b,a%b,x,y),tmp=x;   
        x=y,y=tmp-a/b*y;       
        return gcd; 
    } 
    ll ExCRT() 
    {    
        ll ans=arr[1],M=brr[1];                  
        for(int i=2;i<=n;++i) 
        { 
            ll a=M,b=brr[i],c=arr[i]-ans,gcd,x,y; 
            gcd=exgcd(a,b,x,y),b=abs(b/gcd);    
            x=x*(c/gcd),x=(x%b+b)%b;                              
            ans+=M*x;      
            M*=brr[i]/__gcd(brr[i],M);   
            ans=(ans%M+M)%M; 
        }
        return ans;         
    }
}crt; 
int main()  
{ 
    // setIO("input");   
    int i,j; 
    ll nn,gg,re,tmp,h; 
    scanf("%lld%lld",&nn,&gg); 
    if(gg%(999911659)==0) 
    {
        printf("0
"); 
        return 0;  
    }
    for(i=0;i<4;++i) 
    {
        comb.init(array[i]),re=0,h=nn;  
        for(j=1;j*j<nn;++j) 
        {       
            if(nn%j==0) 
            { 
                re=(re+comb.solve((int)nn,j))%array[i];    
                re=(re+comb.solve((int)nn,nn/j))%array[i];   
            }   
        }      
        if(j*j==nn) re=(re+comb.solve((int)nn,j))%array[i];   
        crt.arr[i+1]=re; 
        crt.brr[i+1]=(ll)array[i];             
    }
    crt.n=4;                            
    tmp=crt.ExCRT();         
    printf("%lld
",qpow(gg,tmp,999911659));          
    return 0; 
}