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;

const int maxn=4e5+7,p=1e9+7;
long long fac[maxn],inv[maxn],ans;
int n,k;

long long poww(long long a,long long b)
{
	long long ans=1,tmp=a;
	while(b) {
		if(b&1) ans=(ans*tmp)%p;
		tmp=(tmp*tmp)%p;
		b>>=1;
	}
	return ans;
}

long long c(int n,int m)
{
	long long ans=fac[n];
	ans=(((ans*inv[m])%p)*inv[n-m])%p;
	return ans;
}

int main()
{
	scanf("%d %d",&n,&k);
	fac[0]=inv[0]=1;
	for(int i=1;i<maxn;++i) fac[i]=(fac[i-1]*i)%p;
	inv[maxn-1]=poww(fac[maxn-1],p-2);
	for(int i=maxn-2;i;--i) inv[i]=(inv[i+1]*(i+1))%p;
	k=min(k,n-1);
	for(int i=0;i<=k;++i) {
		ans+=(c(n,i)*c(n-1,i))%p;
		ans%=p;
	}
	printf("%lld",ans);
}