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 moder = 1000000007;
long long fac[300005];
long long multi(long long a,long long b){
	if(b==0) return 1;
	if(b==1) return a;
	long long ret = multi(a,b/2);
	ret*=ret;
	ret%=moder;
	if(b%2){
		ret*=a;
		ret%=moder;
	}
	return ret;
}
long long C(int n,int r){
	long long down = (fac[r]*fac[n-r])%moder;
	return (fac[n]*multi(down,moder-2))%moder;
}
long long H(int n,int r){
	return C(n+r-1,r);
}
int main(){
	fac[0] = 1;
	for(int i=1; i<=300000; i++){
		fac[i] = fac[i-1]*i;
		fac[i]%=moder;
	}
	long long n,k;
	cin>>n>>k;
	long long can_empty = min(n-1,k);
	long long ret = 0;
	for(int i=0; i<=can_empty; i++){
		ret+=(C(n,i)*H(n-i,i))%moder;
		ret%=moder;
	}
	cout<<ret;
}