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 ll long long
using namespace std;
const int N=4e5+5;
const int MD=1e9+7;
int f[N],inv[N];
int quick_pow(int x,int y) {
	int ans=1;
	while(y) {
		if(y&1) ans=1LL*ans*x%MD;
		y>>=1;
		x=1LL*x*x%MD;
	}
	return ans;
}
int C(int n,int m) {
	return 1LL*f[n]*inv[m]%MD*inv[n-m]%MD;
}
void add(int &x,int y) {
	x+=y;
	if(x>=MD) x-=MD;
}
void init() {
	f[0]=1;
	for(int i=1;i<N;i++) f[i]=1LL*f[i-1]*i%MD;
	inv[N-1]=quick_pow(f[N-1],MD-2);
	for(int i=N-2;i>=0;i--) inv[i]=1LL*inv[i+1]*(i+1)%MD;
}
int main() {
	//freopen("in.txt","r",stdin);
	init();
	int n,k,ans=0;
	scanf("%d%d",&n,&k);
	k=min(k,n-1);
	for(int i=0;i<=k;i++) {
		add(ans,1LL*C(n,i)*C(n-1,i)%MD);
	}
	printf("%d\n",ans);
	return 0;
}
