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
#define MOD 1000000007ll
using namespace std;

int pw[200010],rev[200010];

inline int my_pow(int x,int y)
{
	if(y==0ll) return 1ll;
	if(y==1ll) return x;
	int res=my_pow(x,y/2ll);
	if(y%2ll==0ll) return (res*res)%MOD;
	else return (((res*res)%MOD)*x)%MOD;
}

signed main()
{
	ios::sync_with_stdio(false);
	int n,k;
	cin>>n>>k;
	k=min(k,n-1ll);
	pw[0]=1ll;rev[0]=1ll;
	for(int i=1;i<=n;i++){
		pw[i]=pw[i-1]*i;
		pw[i]%=MOD;
		rev[i]=my_pow(pw[i],MOD-2ll);
	}
	int ans=0ll;
	for(int i=0;i<=k;i++){
		int num1=(pw[n-1]*((rev[i]*rev[n-i-1])%MOD))%MOD;
		int num2=(pw[n]*((rev[i]*rev[n-i])%MOD))%MOD;
		ans+=(num1*num2)%MOD;
		if(ans>=MOD) ans-=MOD;
	}
	cout<<ans<<endl;
	return 0;
}