Lucas定理

Posted 2021-03-25 ukcxrtjr

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
#include<ctime>
#include<queue>
#include<vector>
using namespace std;
const int N=100005;
int n,m,p;
long long A[N+5],B[N+5];
int C(int n,int m,int p){
    if(m>n){
        return 0;
    }
    return A[n]*B[n-m]%p*B[m]%p;
}
int Lucas(int n, int m, int p){
    if(!m){
        return 1;
    }
    return C(n%p, m%p, p)*Lucas(n/p, m/p, p)%p;
}
int main(){
    int t;
    scanf("%d", &t);
    while(t--){
        scanf("%d%d%d",&n,&m,&p);
        A[0]=B[0]=A[1]=B[1]=1;
        n+=m;
        for(int i=2;i<=p;i++){
            B[i]=-(p/i)*B[p%i]%p;
        }
        for(int i=2;i<=p;i++){
            A[i]=A[i-1]*i%p,
            B[i]=B[i-1]*B[i]%p;
        }
        printf("%d
",(Lucas(n,m,p)+p)%p);
    }
    return 0;
}