备战NOIP——模板复习6

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这里只有模板，并不作讲解，仅为路过的各位做一个参考以及用做自己复习的资料，转载注明出处。

卢卡斯定理

/*Copyright: Copyright (c) 2018
*Created on 2018-10-28  
*Author: 十甫
*Version 1.0 
*Title: Lucas
*Time: inf mins
*/ 
#include<iostream>
#include<cstdio>
using namespace std;
typedef long long ll;
const int size = 100005;

ll a, b, p, inv[size], factor[size];
ll Lucas(ll x, ll y) {
	if(x < y) return 0;
	else if(x < p) return factor[x] * inv[y] * inv[x - y] % p;
	else return Lucas(x / p, y / p) * Lucas(x % p, y % p) % p;
}
int main() {
	int T;
	scanf("%d", &T);
	while(T--) {
		scanf("%lld%lld%lld", &a, &b, &p);
		inv[0] = inv[1] = 1;
		for(int i = 2;i <= a + b;i++) {
			inv[i] = inv[p % i] * (p - p / i) % p;
		}
		for(int i = 2;i <= a + b;i++) {
			inv[i] = inv[i - 1] * inv[i] % p;
		}
		factor[0] = factor[1] = 1;
		for(int i = 2;i <= a + b;i++) {
			factor[i] = factor[i - 1] * i % p;
		}
		printf("%lld\n", Lucas(a + b, b));
	}
	return 0;
}