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 int long long
const int mxN=200005,M=1e9+7;
int n,k,resp;
int mod(int x,int M){int ret=x%M;if(ret<0)ret+=M;return ret;}
int fact[mxN],inv[mxN];
int exp(int a,int b,int M){
    if(b==0LL)return 1LL;
    if(b==1LL)return mod(a,M);

    int t=mod(exp(a,b/2,M),M);
    if(b%2==1)return mod(a*mod(t*t,M),M);
    return mod(t*t,M);
}

int C(int n,int k){
    return mod(fact[n]*mod(inv[k]*inv[n-k],M),M);
}

int32_t main(){
    cin>>n>>k;
    fact[0]=inv[0]=1;
    for(int i=1;i<mxN;i++){
        fact[i]=(fact[i-1]*i)%M;

    }
    inv[mxN-1] = exp(fact[mxN-1],M-2,M);
	for(int i=mxN-2;i>=1;i--){
		inv[i] = (inv[i+1]*(i+1))%M;
	}

    for(int i=0;i<=min(n-1,k);i++){
        resp=mod(resp+mod(C(n,i)*C(n-1,i),M),M);
    }
    cout<<resp;


}