There is a building with n rooms, numbered 1 to n.

We can move from any room to any other room in the building.

Let us call the following event a move: a person in some room i goes to another room j~ (i \neq j).

Initially, there was one person in each room in the building.

After that, we know that there were exactly k moves happened up to now.

We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?

Find the count modulo (10^9 + 7).

Constraints

* All values in input are integers.
* 3 \leq n \leq 2 \times 10^5
* 2 \leq k \leq 10^9

Input

Input is given from Standard Input in the following format:


n k


Output

Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).

Examples

Input

3 2


Output

10


Input

200000 1000000000


Output

607923868


Input

15 6


Output

22583772
#include<bits/stdc++.h>

using namespace std;

typedef long long int ll;

const ll mod = 1e9 + 7;
const ll MAXN = 2e5 + 5;

vector < ll > fact(MAXN);

ll pwr(ll a, ll b){
  ll res = 1;
  while(b > 0){
    if(b & 1) res = (res * a) % mod;
    a = (a * a) % mod;
    b >>= 1;
  }
  return res;
}

ll inv(ll a){
  return pwr(a, mod - 2);
}

ll comb(ll n, ll r){
  return (((fact[n] * inv(fact[n - r])) % mod) * inv(fact[r])) % mod;
}

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

  ll n, k;
  cin >> n >> k;

  fact[0] = 1;
  for(int i = 1; i < MAXN; i++) fact[i] = (i * fact[i - 1]) % mod;

  ll ans = 0;
  for(int i = max(n - k, (ll)1); i <= n; i++){
    ans = (ans + ((comb(n - 1, i - 1) * comb(n, i)) % mod)) % mod;
  }

  cout << ans << '\n';
}
