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<iostream>
using namespace std;
const long long m=1e9+7;
long long n,k,x,jc[200005];
void init()
{
	jc[0]=1;
	for(long long i=1;i<=n;i++)
	jc[i]=(jc[i-1]*i)%m;
}
long long qpow(long long a,long long n)
{
	long long ans=1;
	while(n)
	{
		if(n&1) ans=(ans*a)%m;
		a=(a*a)%m;
		n>>=1;
	}
	return ans;
}
long long c(long long n,long long r)
{
	long long ans=1,ans1=1;
	ans1=qpow(jc[n-r],m-2);
	ans=qpow(jc[r],m-2);
	ans=(jc[n]*((ans1*ans)%m))%m;
	return ans;
}
int main()
{
	long long ans3=0;
	cin>>n>>k;
	init();
	if(k>=n)  k=n-1;
	for(long long i=0;i<=k;i++)
	{
		ans3+=(c(n,i)*c(n-1,i))%m;
		ans3%=m;
	}
	ans3=(ans3+m)%m;
	cout<<ans3<<endl;
	return 0;
} 