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;
const long long md=1e9+7;
long long n,k,ft=1,sc=1,nd,ans;
long long pww(long long x,long long y)
{
	nd=1;
	while(x)
	{
		if(x%2==1)
		{
			nd*=y;
			nd%=md;
		}
		y*=y;
		y%=md;
		x/=2;
	}
	return nd;
}
int main()
{
	cin>>n>>k;
	k=min(n-1,k);
	long long nw=n,nww=1;
	for(int i=0;i<=k;i++)
	{
		ans+=ft*sc;
		ans%=md;
//		cout<<ft<<' '<<sc<<endl; 
		sc*=nw;
		sc%=md;
		sc*=pww(md-2,n-nw+1);
		sc%=md;
		ft*=n-nww;
		ft%=md;
		ft*=pww(md-2,nww);
		ft%=md;
		nw--;
		nww++;
	}
	cout<<ans<<endl;
	return 0;
}