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>
#define int long long
using namespace std;
const int mod=1000000007;
int p(int A,int B){
  if(!B)return 1;
  if(B%2)return p(A,B-1)*A%mod;
  int C=p(A,B/2);
  return C*C%mod;
}
int k[1000100];
int c(int A,int B){
  return k[A]*p(k[A-B]*k[B]%mod,mod-2)%mod;
}
signed main(){
  k[0]=1;
  for(int i=1;i<=1000000;i++)k[i]=k[i-1]*i%mod;
  int N,K,ans=0;
  cin>>N>>K;
  for(int i=max(N-K,1LL);i<=N;i++)
    ans=(ans+c(N-1,i-1)*c(N,i)%mod)%mod;
  cout<<ans<<endl;
}