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;
#define MOD 1000000007

long long mod_inv(long long n)
{
    long long left=MOD-2;  // define MOD!
    long long num=n;
    long long ans=1;
    while(left!=0)
    {
        if(left%2==1)ans=(ans*num)%MOD;
        left/=2;
        num=(num*num)%MOD;
    }
    return ans;
}

int main()
{
  long long n,k;cin>>n>>k;
  long long ans=1;
  long long combn=1;
  long long combn1=1;
  int i;
  for(i=1;i<=min(k,n-1);i++)//check
  {
    combn=combn*((n-i+1)*mod_inv(i)%MOD);
    combn%=MOD;
    combn1=combn1*((n-i)*mod_inv(i)%MOD);
    combn1%=MOD;
    ans=(ans+(combn*combn1%MOD))%MOD;
    //cout<<ans<<endl;
  }
  cout<<ans<<endl;
}
