[模板][数学] 卢卡斯定理

https://oi-wiki.org/math/lucas/

# include <iostream>
# include <cstdio>
# define LL long long
# define MAXN 100005

using namespace std;

template<typename T>
T rd(){
	T fl = 1, x = 0;
	int ch = getchar();
	for(	;!isdigit(ch); ch = getchar()){
		if(ch  == '-'){
			fl = -1;
		}
	}
	for(	; isdigit(ch); ch = getchar()){
		x = x * 10 + ch - '0';
	}
	return fl * x;
}

//
LL fac[MAXN];

//
LL QPow(LL x, LL y, LL p){
	LL base = x % p, ans = 1;
	for(	; y; y >>= 1){
		if(y & 1){
			(ans *= base) %= p;
		}
		(base *= base) %= p;
	}
	return ans;
}

LL Inv(LL x, LL p){
	return QPow(x, p-2, p);
}

LL Combine(LL m, LL n, LL p){
	return  m > n ? 0 : fac[n]*Inv(fac[m], p)*Inv(fac[n-m], p)%p;
}

LL Lucas(LL m, LL n, LL p){
	if(!m){
		return 1;
	}
	return m > n ? 1 : Combine(m%p, n%p, p) * Lucas(m/p, n/p, p) % p;
}
//
int main(){	
	fac[0] =  1;

	int T;
	T = rd<int>();
	for(	; T; T--){
		LL n, m, p;
		n = rd<LL>(), m = rd<LL>(), p = rd<LL>();
		for(int i = 1; i <= p; i++){
			fac[i] = fac[i-1]*i%p;
		}

		printf("%lld\n", Lucas(m, n+m, p));
	}
	return 0;
}