Reverse factorial, C++ (gcc)

Reverse factorial

#include <iostream>
#define MAXTAM 20
int MOD=1000000000+7;

using namespace std;

typedef long long ll;

ll rev_fact[MAXTAM];
ll fact[MAXTAM];

ll fast_pow(ll x, ll y)
{
    ll resp = 1, tmp = x;
    while(y)
    {
        if(y & 1)
            resp = (resp * tmp) % MOD;
        
        tmp = (tmp * tmp) % MOD;
        y >>= 1;        
    }
    return resp;
}

void factorial()
{
    fact[0] = 1;
    fact[1] = 1;
    fact[2] = 2;
    
    for(int i = 3; i <= MAXTAM+1; i++)
    {
        fact[i] =( i * fact[i-1])%MOD;
        //cout << i << ") " << fact[ i] << "\n";
    }
}

int main()
{
    int n, k;
    
    factorial();
    
    rev_fact[MAXTAM-1] = (fast_pow(fact[MAXTAM], MOD-2)*MAXTAM)%MOD;
    //cout << fast_pow(fact[MAXTAM], MOD-2);
        
    for(int i = MAXTAM-2; i >= 0; i--)
        rev_fact[i] = ((i + 1) * rev_fact[i + 1]) % MOD;

cin >> n;
    cin >> k;

/*for(int i=1; i<MAXTAM; i++)
        cout << rev_fact[i] <<"\n";*/

cout << (fact[n]*((rev_fact[k]*rev_fact[n-k])%MOD))%MOD;
    // cout << fast_pow( 12, 8, 7);
    // cout << fact[4];
}


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