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<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<cstring>
#include<string>
using namespace std;
int mod=1000000007;
int jc[200005]={1},ny[200005]={1};
int n,k; 
int Power(int x,int y,int mod) {
	int ret=1;
	while(y) {
		if(y&1)ret=1ll*ret*x%mod;
		x=1ll*x*x%mod,y>>=1;
	}
	return ret;
}
int C(int n,int m){
	return 1ll*jc[n]*ny[m]%mod*ny[n-m]%mod;
}
int F(int k){
	for(int i=1;i<=n;i++)jc[i]=1ll*jc[i-1]*i%mod,ny[i]=Power(jc[i],mod-2,mod);
	int ans=1;
	for(int i=1;i<=k;i++)ans=(ans+1ll*C(n,i)*C(n-1,i))%mod;
	return ans;
}
int main(){
	cin>>n>>k;
	if(k>=n-1)k=n-1;
	if(k==1)cout<<1ll*n*(n-1)%mod;
	else cout<<F(k)<<endl;
}