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;
  vector<long>kai(200001);
long ncrmodp(int n,int r,long p){
  long ans = 1;
  long tmp = 1;
  int i;

  ans = kai[n];
  tmp = (kai[r]*kai[n-r])%p;


  for(long bit = 1;bit<=p-2;bit*=2){
    if(bit & p-2){
      ans *= tmp;
      ans %= p;
    }
    tmp = tmp* tmp;
    tmp %= p;
  }
  return ans;
}

int main(){
  long n,k;
  cin >> n >> k;
  long p = 1000000007;
  int i;
  kai[0]=1;
  for(i=1;i<=n;i++){
    kai[i]=kai[i-1]*i;
    kai[i]%=p;
  }
  vector<long>nc(n+1);
  vector<long>nc1(n);
  for(i=0;i<n;i++){
    nc[i]=ncrmodp(n,i,p);
    nc1[i]=ncrmodp(n-1,i,p);
  }
  nc[n]=1;


  if(k>=n)k=n-1;
  long ans = 1;
  for(i=1;i<=k;i++){
    ans += nc[i]*nc1[i];
    ans %= p;
  }
  cout << ans << endl;








}
