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 <algorithm>
using namespace std;
typedef long long ll;


int main(void){
  int n,k,i;
  ll fac[200005],inv[200005],finv[200005],vyt,ans=0;
  const int mod=1e9+7;
  
  cin >> n >> k;
  
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for (i=2;i<=n+2;i++){
    fac[i]=fac[i-1]*i%mod;
    inv[i]=mod-inv[mod%i]*(mod/i)%mod;
    finv[i]=finv[i-1]*inv[i]%mod;
  }
  
  for (i=0;i<min(n,k+1);i++){
    vyt=fac[n]*finv[i]%mod*finv[n-i]%mod;
    vyt=vyt*fac[n-1]%mod*finv[n-i-1]%mod*finv[i]%mod;
    ans=(ans+vyt)%mod;
  }
  
  cout << ans << endl;
  
  return 0;
}