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 INF 1000000000
#define LINF 1000000000000000000
#define MOD 1000000007
#define mod 1000007
#define INF63 1061109567
#define INF127 9187201950435737471
#define F first
#define S second
#define ll long long
#define N 200010
using namespace std;
ll n,k,ans=0,fct[N];
ll ksm(ll x,ll y)
{
	if(y==0)
	{
		return 1;
	}
	if(y==1)
	{
		return x;
	}
	ll ret=ksm(x,y/2);
	if(y%2==1)
	{
		return ((ret*ret)%MOD*x)%MOD;
	}
	return (ret*ret)%MOD;
}
ll com(ll a,ll b)
{
	b=min(n,a-b);
	return ((fct[a]*ksm(fct[b],MOD-2))%MOD*ksm(fct[a-b],MOD-2))%MOD;
}
int main(){
	ll i,t;
	cin>>n>>k;
	fct[0]=1;
	for(i=1;i<=n;i++)
	{
		fct[i]=(fct[i-1]*i)%MOD;
	}
	for(i=n;i>=max(n-k,(ll)1);i--)
	{
		ans=(ans+(com(n,i)*com(n-1,i-1))%MOD)%MOD;
	}
	cout<<ans<<endl;
	return 0;
}