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 int N=2e5+20,MOD=1e9+7;

int n,k,f[N],ie[N],ans;

int mul(int a,int b) {return (1ll*a*b)%MOD;}

int power(int a,int b)
{
	int num=a,ans=1;
	while(b)
	{
		if(b&1) ans=mul(ans,num);
		b>>=1;
		num=mul(num,num);
	}
	return ans;
}

int inverse_euler(int n)
{
	return power(n,MOD-2);
}

int ncr(int n,int r)
{
	return mul(f[n],mul(ie[r],ie[n-r]));
}

void precompute()
{
	f[0]=1;
	for(int i=1;i<N;i++) f[i]=mul(f[i-1],i);
	for(int i=0;i<N;i++) ie[i]=inverse_euler(f[i]);
}

int main()
{
	precompute();
	cin>>n>>k;
	k=min(k,n-1);

	for(int i=0;i<=k;i++)
		ans=(ans+mul(ncr(n,i),ncr(n-1,n-i-1)))%MOD;
	printf("%d",ans);
}