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 int long long
using namespace std;
const int maxlen=200000;

int n,k,mod=1e9+7,ans=0ll;
int jc[5*maxlen+5];

int quick_power(int a,int b)
{
	int res=1;
	for (;b;b=b>>1,a=(a*a)%mod)
	{
		if (b&1)  res=(res*a)%mod;
	}
	return res;
}

int ny(int n)
{
	return quick_power(n,mod-2)%mod;
}

int C(int n,int k)
{
	if (k<=0||n==k)  return 1;
	if (2*k>n)  k=n-k;
	
	return ((jc[n]*ny(jc[n-k])%mod)*ny(jc[k]))%mod;
}

inline void get_all_jc()
{
	jc[0]=1;
	for (int i=1;i<=5*maxlen;i++)  jc[i]=(jc[i-1]*i)%mod;
}

signed main()
{
	cin>>n>>k;
	get_all_jc();
	
	if (k>n)  return cout<<C(2*n-1ll,n)<<endl,0;
	else
	{
		ans=C(2*n-1ll,n);
		for (int i=1;i<=n-k-1;i++)  ans=((ans-C(n,i)*C(n-1,i-1))%mod+mod)%mod;
		return cout<<ans<<endl,0;
	}
}