сочетания для больших чисел

/*
 ________    _______   ______    _______   ________
/_______/\ /_______/\ /_____/\ /_______/\ /_______/\
\::: _  \ \\::: _  \ \\:::_ \ \\::: _  \ \\::: _  \ \
 \::(_)  \ \\::(_)  \/_\:\ \ \ \\::(_)  \/_\::(_)  \ \
  \::   \ \\::  _  \ \\:\ \ \ \\::  _  \ \\::   \ \
   \:.\ \  \ \\::(_)  \ \\:\_\ \ \\::(_)  \ \\:.\ \  \ \
    \__\/\__\/ \_______\/ \_____\/ \_______\/ \__\/\__\/

*/

#include <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <memory.h>
#include <stdio.h>
#include <stack>
#include <deque>
#include <queue>
#include <set>
#include <iterator>
#include <map>
#include <iomanip>
#include <unordered_set>
#define int long long
#define pb push_back
#define double long double
#define endl "\n"
#define un unsigned
#define INF 1000000009
#define pii pair<int, int>
#define all(v) v.begin(), v.end()
using namespace std;

const int N = 1000000;
const int MOD = 1e9 + 7;

int bin_pow(int n, int i)
{
    if (i == 0)
    {
        return 1;
    }

    if (i == 1)
    {
        return n;
    }

    if (i % 2 == 0)
    {
        return (bin_pow((n * n) % MOD, i / 2)) % MOD;
    }
    else
    {
        return (n * bin_pow(n, i - 1)) % MOD;
    }
}

signed main()
{
    ios_base::sync_with_stdio();
    cin.tie(0);
    cout.tie(0);

    int n, k;
    cin >> n >> k;

    n--;
    k--;

    n += k;

    int ans = 1;

    vector<int> fac(n + 5), rfac(n + 5);

    fac[0] = 1;

    for (int i = 1; i <= 1 + n; i++)
    {
        fac[i] = fac[i - 1] * i;
        fac[i] %= MOD;
    }

    rfac[n] = bin_pow(fac[n], MOD - 2);
    rfac[1] = 1;

    for (int i = n - 1; i >= 0; i--)
    {
        rfac[i] = (rfac[i + 1] * (i + 1)) % MOD;
    }

    cout << ((fac[n] * rfac[k]) % MOD * rfac[n - k]) % MOD;
    return 0;
}