toj 4111 组合数取模 暴力分解

题目大意：组合数取模，n和m并不算大，p比较大且是合数。

思路：暴力分解+快速幂

注：暴力也是有区别的，分解质因数时可以用以下work函数，写的非常巧妙，摘录自互联网。

#include <iostream>
#include <cstring>
using namespace std;

typedef long long ll;
const ll mod = 1ll << 32;
const int N = 1000001;
const int M = 100007;
bool is_prime[N];
int prime[M];
int p;

void get()
{
    memset( is_prime, true, sizeof(is_prime) );
    is_prime[0] = is_prime[1] = false;
    for ( int i = 2; i < N; i++ )
    {
        if ( is_prime[i] )
        {
            int j = i * i;
            if ( j >= N ) break;
            do
            {
                is_prime[j] = false;
                j += i;
            } while ( j < N );
        }
    }
    p = 0;
    for ( int i = 0; i < N; i++ )
    {
        if ( is_prime[i] )
        {
            prime[p++] = i;
        }
    }
}

ll pow_mod( ll a, ll n )
{
    ll ans = 1;
    a = a % mod;
    while ( n )
    {
        if ( n & 1 )
        {
            ans = ans * a % mod;
        }
        n = n >> 1;
        a = a * a % mod;
    }
    return ans;
}

ll work( ll n, ll q )
{
    ll ans = 0;
    while ( n )
    {
        ans += n / q;
        n /= q;
    }
    return ans;
}

ll c( ll n, ll m )
{
    ll ans = 1;
    for ( int i = 0; i < p && prime[i] <= n; i++ )
    {
        ll x = work( n, prime[i] );
        ll y = work( n - m, prime[i] );
        ll z = work( m, prime[i] );
        x = x - ( y + z );
        ans = ans * pow_mod( prime[i], x ) % mod;
    }
    return ans;
}

int main ()
{
    get();
    int t;
    cin >> t;
    while ( t-- )
    {
        ll n, m;
        cin >> n >> m;
        cout << c( n, m ) << endl;
    }
    return 0;
}