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;

typedef long long ll;
const int N = 2e5;
const ll mod = 1e9+7;
ll fact[N+100],inv[N+100];

ll bigmod(ll a,ll b)
{
	if(b==0){
		return 1;
	}
	ll x =  bigmod(a,b/2);
	x = (x*x)%mod;
	if(b%2){
		x = (x*a)%mod;
	}
	return x;
}
int main()
{
	fact[0] = inv[0] = 1;
	for(int i=1;i<=N;i++){
		fact[i] = (fact[i-1]*i)%mod;
		inv[i] = bigmod(fact[i],mod-2);
	}
	int n,k;
	scanf("%d%d",&n,&k);
	ll ans = 0;
	for(int i=0;i<=min(n-1,k);i++){
		ll t1 = (fact[n]*inv[i])%mod;
		t1 = (t1*inv[n-i])%mod;
		int m = n-i;
		ll t2 = (fact[n-1]*inv[m-1])%mod;
		t2 = (t2*inv[n-m])%mod;
		ll t3 = (t1*t2)%mod;
		ans = (ans+t3)%mod;
	}
	printf("%lld\n",ans);
}
