HDU 3037 Saving Beans 多重集合的结合 lucas定理

#include <iostream>
#include <cstdio>
#include <string>
#include <vector>
#include <cstring>
#include <iterator>
#include <cmath>
#include <algorithm>
#include <stack>
#include <deque>
#include <map>
#define lson l, m, rt<<1
#define rson m+1, r, rt<<1|1
#define mem0(a) memset(a,0,sizeof(a))
#define sca(x) scanf("%d",&x)
#define de printf("=======\n")
typedef long long ll;
using namespace std;

const int maxn = 100005;
ll n, m, p;
ll f[maxn];

void init( ll p ) {
    f[0] = 1;
    for( int i = 1; i <= p; i++ ) {
        f[i] = f[i-1] * i % p;
    }
}

ll q_power(ll a, ll b, ll p) {
    ll ret = 1;
    while( b ) {
        if( b & 1 ) ret = ret * a % p;
        b >>= 1;
        a = a * a % p;
    }
    return ret % p;
}

ll lucas( ll n, ll m, ll p ) {
    ll ans = 1;
    while( n && m ) {
        ll nn = n % p, mm = m % p;
        if( nn < mm ) return 0;
        ans = ans * f[nn] * q_power(f[mm]*f[nn-mm]%p, p-2, p) % p;
        n /= p;
        m /= p;
    }
    return ans;
}

int main() {
    int t;
    sca(t);
    while( t-- ) {
        scanf( "%I64d%I64d%I64d", &n, &m, &p );
        init(p);
        printf( "%I64d\n", lucas(n+m, n, p) );
    }
    return 0;
}