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;
const long long mod=1000000007;
long long g(long long p){
    long long x=1;
    for(int i=mod-2;i>0;i/=2){
        if(i%2)x=x*p%mod;
        p=p*p%mod;
    }
    return x;
}
int main(){
    int n,k;
    cin>>n>>k;
    long long x=1,y=1,ans=1;
    for(int i=1;i<=min(n-1,k);i++){
        x=(x*(n-i+1))%mod*g(i)%mod;
        y=(y*(n-i))%mod*g(i)%mod;
        ans=(ans+x*y)%mod;
    }
    cout<<ans<<endl;
    return 0;
}
