【luogu P3807 卢卡斯定理】 模板

题目链接：https://www.luogu.org/problemnew/show/P3807

Lucas定理用来求大组合数对一个质数取模的值，不大于10^5用逆元，大于10^5就用Lucas转化成10^5以内，如果不是质数还要用扩展Lucas

Lucas(n,m,p) = C(n%p,m%p)*Lucas(n/p,m/p,p)

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 100010;
int n, m, p, T;
long long a[maxn], b[maxn];
long long Lucas(int n, int m, int p)
{
    if(n < m) return 0;
    else if(n < p) return b[n]*a[m]*a[n-m]%p;
    else return Lucas(n%p,m%p,p)*Lucas(n/p,m/p,p)%p;
}
int main()
{
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d%d",&n,&m,&p);
        a[0] = 1, a[1] = 1, b[0] = 1, b[1] = 1;
        for(int i = 2; i <= m+n; i++) b[i] = b[i-1]*i%p;
        for(int i = 2; i <= m+n; i++) a[i] = (p-p/i)*a[p%i]%p;
        for(int i = 2; i <= m+n; i++) a[i] = a[i-1]*a[i]%p;
        printf("%lld
",Lucas(n+m,m,p));
    }
    return 0;
}