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>
#include <cstdio>
#include <cstdlib>
using namespace std;
const int mo=1e9+7;
const int maxn=1e6+10;
int n,m;
long long p[maxn],inv[maxn],ans;
long long po(long long a,long long b)
{
	if (b==0) return 1;
	if (b==1) return a%mo;
	long long c=po(a,b/2);
	if (b&1) return c*c%mo*a%mo;else return c*c%mo;
}
long long C(int n,int m){return p[n]*inv[m]%mo*inv[n-m]%mo;}
long long calc(int k,int n){return C(n+k-1,k-1);}
int main()
{
	scanf("%d%d",&n,&m); ans=1;
	p[0]=1; for (int i=1;i<=400000;i++) p[i]=p[i-1]*i%mo;
	inv[400000]=po(p[400000],mo-2);
	for (int i=399999;i>=0;i--) inv[i]=inv[i+1]*(i+1)%mo;
	for (int i=1;i<=min(n-1,m);i++) ans=(ans+C(n,i)*calc(n-i,i)%mo)%mo;
	printf("%lld\n",ans);
return 0;
}