学步园

大整数取模，lucas 定理

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
#define LL __int64
LL n,m,p;
LL Quick_Mod(LL a,LL b,LL mod){
    LL r = 1;
    while(b){
        if(b & 1) r = (r * a) % mod;
        a = (a * a) % mod;
        b >>= 1;
    }
    return r;
}
LL Cm(LL n,LL m,LL p){
    LL a,b,r = 1;
    for(LL i = 1;i <= m;i++){
        a = (n + i - m) % p;
        b = i % p;
        r = r *(a * Quick_Mod(b,p - 2,p) % p) % p;
    }
    return r;
}
LL Lucas(LL n,LL m,LL p){
    if(m == 0) return 1;
    return (Lucas(n/p,m/p,p) * Cm(n % p,m % p,p)) % p;
}
int main(){
    int T;
    while(~scanf("%d",&T)){
        while(T--){
            scanf("%I64d%I64d%I64d",&n,&m,&p);
            printf("%I64d\n",Lucas(n,m,p));
        }
    }
    return 0;
}