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 <iostream>
#include <vector>

using namespace std;

typedef long long ll;
const ll mod = 1e9 + 7;
ll fac[200005];
ll rfac[200005];


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


int main() {
  ll n,k;
  cin >> n >> k;

  fac[0] = rfac[0] = 1;
  
  for(ll i = 1; i <= n; i++) {
    fac[i] = fac[i-1] * i % mod;
    rfac[i] = f(fac[i],mod-2);
  }

  ll ans = 1;
  for(ll i = 1; i <= min((ll)(n-1),k); i++) {
    ans = (ans + fac[n] * rfac[i] % mod * rfac[n-i] % mod * fac[n-1] % mod *  rfac[n-i-1] % mod * rfac[i] % mod) % mod;
  }
  cout << ans << endl;
}



  
  
