C++ Combinatorics Template

#include <iostream>
#include <vector>

using namespace std;

long long MOD = 1e9+7;

long long fast_pow(long long a, int p)
{
  if(p == 0) return 1;
  long long half = fast_pow(a, p/2);
  if(p%2 == 0) return half * half % MOD;
  return a * half % MOD * half % MOD;
}


struct matrix
{
    int n,m;
    vector<vector<long long>> arr;

    matrix(int n)
    {
        this->n = this->m = n;
        arr.assign(n, vector<long long>(m));
    }
    matrix(int n, int m)
    {
        this->n = n; this->m = m;
        arr.assign(n, vector<long long>(m));
    }
    matrix(vector<vector<long long>>& arr)
    {
        this->arr = arr;
        n = arr.size();
        m = arr[0].size();
    }
    vector<long long>& operator [](int i)
    {
        return arr[i];
    }
};

matrix ident(int n)
{
    matrix I(n);
    for(int i=0;i<n;i++) I[i][i] = 1;
    return I;
}

matrix mmult(matrix& A, matrix& B)
{
    matrix C(A.n, B.m);
    for(int i=0;i<A.n;i++) for(int j=0;j<B.m;j++) for(int k=0;k<A.m;k++) {C[i][j] += (A[i][k] * B[k][j]) % MOD; C[i][j] %= MOD;}
    return C;
}

matrix mpow(matrix& A, long long p)
{
    if(p==0) return ident(A.n);
    matrix half = mpow(A, p/2);
    matrix res = mmult(half, half);
    if(p&1) return mmult(A, res);
    return res;
}

vector<long long> fact(3e5);

void comp_fact()
{
  fact[0] = 1;
  for(int i=1;i<fact.size();i++)
     fact[i] = i * fact[i-1] % MOD;
}

long long inverse_mod(int n){ return  fast_pow(n, MOD - 2); }

long long C(int n, int k)
{
  if(k > n) return 0;
  return fact[n] * inverse_mod(fact[k]) % MOD * inverse_mod(fact[n - k]) % MOD;
}