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;
using ll = long long;

const int M = 1e9+7;

int mul(int x, int y){
    return 1LL*x*y%M;
}

int add(int x, int y){
    return (x%M+y%M)%M;
}



int main(){
    int n,k;cin>>n>>k;
    k = min(k,n-1);
    vector<int> fact(2*n),inv(2*n),ifact(2*n);
   
    fact[0] = ifact[0] = inv[1] = fact[1] = ifact[1] = 1;

    for(int i = 2; i < 2*n; i++){
        fact[i] = mul(fact[i-1],i);
        inv[i] = (M - mul(M/i,inv[M%i]))%M;
        ifact[i] = mul(ifact[i-1],inv[i]);
    }
    ll ans = 0;
    
    auto C = [&](int n, int k){
        if(n<=0 || k<=0) return 1;
        
        return mul(fact[n],mul(ifact[k],ifact[n-k]))%M;
    };

    for(int i = 0 ; i <= k ; i++){
        int x = n-i;
        ans+=mul(C(n,i),C(n-1,x-1));
    }
    cout<<ans%M;
}
