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 mod 1000000007
#define int long long
using namespace std;
const int N=2*1e5+100;
int n,k,fac[N*2],inv[N*2];
int m_pow(int a,int b)
{
	int ans=1;
	while (b)
	{
		if (b&1) ans=ans*a%mod;
		b>>=1;
		a=a*a%mod;
	}
	return ans;
}
int C(int n,int m)
{
	return (fac[n]*inv[m]%mod)*inv[n-m]%mod;
}
signed main()
{
	scanf("%lld%lld",&n,&k);
	fac[1]=1;
	for (int i=2;i<=2*n;i++) fac[i]=(fac[i-1]*i)%mod;
	inv[2*n]=m_pow(fac[2*n],mod-2);
	for (int i=2*n-1;i>=1;i--) inv[i]=(i+1)*inv[i+1]%mod;
	if (k>=n-1)
	{
		printf("%lld\n",C(2*n-1,n-1));
		return 0;
	}
	else
	{
		int ans=1;
		for (int i=1;i<=k;i++)
		  ans=(ans+C(n-1,n-i-1)*C(n,i)%mod)%mod;
		printf("%lld\n",ans);
	}
}