HDU 3073 Saving Beans

Saving Beans

Time Limit: 3000ms

Memory Limit: 32768KB

This problem will be judged on HDU. Original ID: 3037
64-bit integer IO format: %I64d      Java class name: Main

 

Although winter is far away, squirrels have to work day and night to save beans. They need plenty of food to get through those long cold days. After some time the squirrel family thinks that they have to solve a problem. They suppose that they will save beans in n different trees. However, since the food is not sufficient nowadays, they will get no more than m beans. They want to know that how many ways there are to save no more than m beans (they are the same) in n trees.

Now they turn to you for help, you should give them the answer. The result may be extremely huge; you should output the result modulo p, because squirrels can’t recognize large numbers.

 

Input

The first line contains one integer T, means the number of cases.

Then followed T lines, each line contains three integers n, m, p, means that squirrels will save no more than m same beans in n different trees, 1 <= n, m <= 1000000000, 1 < p < 100000 and p is guaranteed to be a prime.

 

Output

You should output the answer modulo p.

 

Sample Input

2
1 2 5
2 1 5

Sample Output

3
3


解题：Lucas 求组合数取模

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
LL F[100010] = {1};
void init(LL mod) {
    for(int i = 1; i <= mod; ++i)
        F[i] = F[i-1]*i%mod;
}
LL gcd(LL a,LL b,LL &x,LL &y) {
    if(!b) {
        x = 1;
        y = 0;
        return a;
    }
    LL ret = gcd(b,a%b,y,x);
    y -= x*(a/b);
    return ret;
}
LL Inv(LL b,LL mod) {
    LL x,y,d = gcd(b,mod,x,y);
    return d == 1?(x%mod + mod)%mod:-1;
}
LL inv(LL b,LL mod) {
    if(b == 1) return 1;
    return inv(mod%b,mod)*(mod-mod/b)%mod;
}
LL Lucas(LL n,LL m,LL mod) {
    LL ret = 1;
    while(n && m) {
        LL a = n%mod;
        LL b = m%mod;
        if(a < b) return 0;
        ret = ret*F[a]%mod*Inv(F[b]*F[a-b]%mod,mod)%mod;
        n /= mod;
        m /= mod;
    }
    return ret;
}
int main() {
    int kase,n,m,mod;
    scanf("%d",&kase);
    while(kase--) {
        scanf("%d%d%d",&n,&m,&mod);
        init(mod);
        printf("%I64d
",Lucas(n+m,n,mod));
    }
    return 0;
}