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;

long long MOD=1000000007;

long long fac[2000002],finv[2000002],inv[2000002];

void COMinit(){
	fac[0]=fac[1]=1;
	finv[0]=finv[1]=1;
	inv[1]=1;
	for(int i=2;i<2000002;i++){
		fac[i]=fac[i-1]*i%MOD;
		inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
		finv[i]=finv[i-1]*inv[i]%MOD;
	}
}
 
long long COM(int n,int k){
	if(n<k)return 0;
	if(n<0 || k<0)return 0;
	return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

int main(){
	COMinit();
	int n,k;
	cin >> n >> k;
	
	long long ans=0;
	
	for(int i=0;i<=min(n,k);i++){
		long long add=COM(n,i);
		add*=COM(n-i-1+i,i);
		add%=MOD;
		ans+=add;
		ans%=MOD;
	}
	
	cout << ans << endl;
	return 0;
}