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>
#include<vector>
using namespace std;
typedef long long ll; 
const ll mod=1e9+7;
ll fact[300005]={0};
ll qpow(ll a,ll b)
{
	if(b==0)
	{
		return 1;
	}
	else if(b==1)
	{
		return a;
	}
	else if(b%2==0)
	{
		ll c=qpow(a,b/2);
		return c*c%mod;
	}
	else
	{
		ll c=qpow(a,b/2);
		return ((c*c)%mod*a)%mod;
	}
}
ll cnk(ll n,ll k)
{
	ll b=fact[n-k]*fact[k];
	b%=mod;
	return fact[n]*qpow(b,mod-2)%mod;
}
int main(void)
{
	ll n,k;
	scanf("%lld%lld",&n,&k);
	if(k>=n)
	{
		k=n-1;
	}
	fact[0]=fact[1]=1;
	for(ll i=2;i<=n+100000;i++)
	{
		fact[i]=fact[i-1]*i;
		fact[i]%=mod;
	}
	ll ans=0;
	for(ll i=0;i<=k;i++)
	{
		ans+=cnk(n,i)*cnk(n-1,i);
//		printf("%lld %lld %lld %lld\n",n,i,cnk(n,i),cnk(n-1,i));
		ans%=mod;
	}
	printf("%lld",ans);
}