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<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int MAXN = 2e5 + 5;
const int mod = 1e9 + 7;

inline ll pw(ll a,int b)
{
	ll res=1;
	while(b)
	{
		if(b&1) res=res*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return res;
}

ll fac[MAXN],inv[MAXN];

inline ll c(int n,int m)
{
	if(n<0||m<0||n<m) return 0;
	return fac[n]*inv[m]%mod * inv[n-m] %mod;
}

int main(void)
{
	fac[0]=1;
	for(int i=1; i<MAXN; ++i) fac[i] = fac[i-1]*i %mod;
	inv[MAXN-1]=pw(fac[MAXN-1],mod-2);
	for(int i=MAXN-2; i>=0; --i) inv[i] = inv[i+1]*(i+1) %mod;
	
	int n,d;
	scanf("%d%d",&n,&d);
	if(d>n) d=n;
	
	int ans=0;
	for(int i=0; i<=d; ++i)
	{
		ans += c(n,i) * c(n-1,n-i-1) %mod;
		if(ans>=mod) ans-=mod;
	}
	printf("%d",ans);
	return 0;
}