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>
using namespace std;
const int P=1e9+7,MAXN=200010;
int n,k,ans,fac[MAXN],inv[MAXN];
int qpow (int a,int b) {
	int res=1;
	while (b) {
		if (b&1) {res=(1ll*res*a)%P;}
		a=(1ll*a*a)%P,b>>=1;
	}
	return res;
}
void init () {
	fac[0]=inv[0]=1;
	for (int i=1;i<=n;i++) {fac[i]=(1ll*fac[i-1]*i)%P;}
	inv[n]=qpow(fac[n],P-2);
	for (int i=n-1;i>=1;i--) {inv[i]=(1ll*inv[i+1]*(i+1))%P;}
	return;
}
int c (int n,int m) {return (1ll*fac[n]*((1ll*inv[m]*inv[n-m])%P))%P;}
int main () {
	scanf("%d%d",&n,&k);
	init();
	for (int i=0;i<=min(n-1,k);i++) {
		ans=(ans+(1ll*c(n,i)*c(n-1,i))%P)%P;
	}
	printf("%d\n",ans);
	return 0;
}