1067 - Combinations---LightOj（Lucas求组合数）

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <math.h>

using namespace std;

#define met(a, b) memset(a, b, sizeof(a))
#define N 1000953
#define INF 0x3f3f3f3f
const int MOD = 1000003;

typedef long long LL;

LL f[N];

LL Pow(LL a, LL b)
{
    LL ans = 1;
    while(b)
    {
        if(b&1)
            ans = ans*a%MOD;
        b>>=1;
        a = a*a%MOD;
    }
    return ans;
}

LL C(LL n, LL m)
{
    if(m == 0)return 1;
    if(m > n)return 0;
    /*
    LL ans = 1;
    for(int i=1; i<=m; i++)
    {
        LL a = (n-m+i);
        LL b = i;
        ans = ans*(a*Pow(b, MOD-2)%MOD)%MOD;
    }这样会超时，所以要预处理阶乘；
    */
///C(n, m) = n!/(m!(n-m)!)%MOD--->n!/m!%MOD * 1/((n-m)!)%MOD;
///   a/b%MOD == a*b^(MOD-2)%MOD;
    LL ans = f[n]*Pow(f[m], MOD-2)%MOD * 1*Pow(f[n-m], MOD-2) % MOD;

    return ans;
}

void Fact(LL n)
{
    f[0] = 1;
    for(int i=1; i<=n; i++)
        f[i] = f[i-1]*i%MOD;

}

int main()
{
    Fact(MOD);
    int T, t = 1;
    LL n, k;
    scanf("%d", &T);
    while(T--)
    {
        scanf("%lld %lld", &n, &k);
        LL ans = C(n, k);
        printf("Case %d: %lld\n", t++, ans);
    }
    return 0;
}