求组合数

#include <cstdio>
using namespace std;

#define MAX_NUMBER 100000
//快速幂求x^n%mod
long long quick_pow(long long x, long long n, long long mod)
{
    long long res = 1;
    while (n)
    {
        if (n & 1)
        {
            res = res * x % mod;
        }

        x = x * x % mod;
        n >>= 1;
    }

    return res;
}

long long fac[MAX_NUMBER+5];
long long n, m, p;

int main()
{
    while (~scanf("%lld %lld %lld", &n, &m, &p))
    {
        //预处理求fac，fac[i] = i!%p
        fac[0] = 1;
        for (int i = 1; i <= n; i++)
        {
            fac[i] = fac[i - 1] * i % p;
        }
        //组合数 = n!*(m!%p的逆元)*((n-m)!%p的逆元)%p
        printf("%lld\n", fac[n] * quick_pow(fac[m], p - 2, p) % p * quick_pow(fac[n - m], p - 2, p) % p);
    }
}