欧拉公式 大组合数 2017 ICPC 乌鲁木齐 D Fence Building

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;
typedef long long ll;
const long long int mod=1e9+7;
 
ll mod_pow(ll x, ll n, ll p){ //快速幂 
    ll res = 1;
    while(n){
        if(n & 1) res =res * x % p;
        x = x * x % p;
        n >>= 1;
    }
    return res;
}
 
ll comb(ll n, ll m, ll p){ //comb用来求解组合数 
    if(m > n) return 0;
    ll ret = 1;
    m = min(n - m, m);
    for(int i = 1; i <= m; i ++){
        ll a = (n + i - m) % p;
        ll b = i % p;
        ret = ret * (a * mod_pow(b, p - 2, p) % p) % p;
    }
    return ret;
}
 
ll Lucas(ll n, ll m, ll p){  //卢卡斯定理---处理大的组合数对素数取模的情况，因为这时如果递推的话将会特别耗时 
    if(m == 0) return 1;
    return comb(n % p, m % p, p) * Lucas(n / p, m / p, p) % p;
}
 
int main(){
    int T;
    ll n, m, p;
    scanf("%d", &T);
    int cas=1;
    while(T--){
        scanf("%lld",&n);
        
        long long ans=(Lucas(n,2,mod)+Lucas(n,4,mod)+1)%mod;
        printf("Case #%d: %lld\n",cas++,ans);
    }
    return 0;
}