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>
using namespace std;
const long long mod=1000000007,NR=1145140;
long long n,k,ans,a[NR];
long long power(long long x,long long y)
{
	if(y==0)
	{
		return 1;
	}
	long long tmp=power(x,y>>1),ans=(tmp*tmp)%mod;
	if(y&1)
	{
		ans=(ans*x)%mod;
	}
	return ans;
}
long long c(long long n,long long k)
{
	return (a[n]*power((a[k]*a[n-k])%mod,mod-2))%mod;
}
int main()
{
	scanf("%lld%lld",&n,&k);
	a[0]=1;
	for(long long i=1;i<2*n;i++)
	{
		a[i]=(a[i-1]*i)%mod;
	}
	ans=c(2*n-1,n);
	for(long long i=1;i<n-k;i++)
	{
		ans=(ans-((c(n,i)*c(n-1,i-1))%mod))%mod;
	}
	printf("%lld",(ans+mod)%mod);
	return 0;
}