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 ll long long
#define p 1000000007
using namespace std;
ll f[200005],ni[200005];
ll quickpow(ll a,ll b)
{
	ll res=1;
	while(b)
	{
		if(b&1)
		res=res*a%p;
		a=a*a%p;
		b>>=1;
	}return res;
}
ll zuhe(ll n,ll m)
{		ll sum;
	sum=f[n]*ni[n-m]%p*ni[m]%p;
	return sum;
}
int main()
{
	ll n,k;scanf("%lld%lld",&n,&k);
	ll a=min(k,n-1);ll sum=1;
	f[0]=1;ni[0]=quickpow(f[0],p-2)%p;
	for(int i=1;i<=n;++i) 
	{
	f[i]=f[i-1]*i%p;ni[i]=quickpow(f[i],p-2)%p;	
	}
	for(int i=1;i<=a;++i)
	{
	sum=(sum+zuhe(n,i)*zuhe(n-1,i)%p)%p;
		
	}
	printf("%lld",sum);
}