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;
//mt19937 mrand(chrono::high_resolution_clock::now().time_since_epoch().count());
//int rnd(int x) { return mrand()%x;}
typedef long long ll;
ll gcd(ll a,ll b){return b==0?a:gcd(b,a%b);}
const ll md=1e9+7;
ll qp(ll a,ll b){
	ll ret=1;
	if(a==0) return ret;
	while(b){
		if(b&1) ret=ret*a%md;
		a=a*a%md;
		b>>=1;
	}
	return ret;
}
ll c1[200200],c2[200200];
void C(ll c[],ll x){
	ll ret=1;
	c[0]=c[x]=1;
	for(ll i=1;i<x;i++){
		ret=ret*(x-i+1)%md;
		ret=ret*qp(i,md-2)%md;
		c[i]=ret;
	}
	return;
}
int main(){
	int n,k;
	scanf("%d%d",&n,&k);
	ll ans=0;
	C(c1,n);
	C(c2,n-1);
	for(int i=0;i<n;i++){
		if(i>k ) continue;
		ans=(ans+c1[i]*c2[i]%md)%md;
	}
	printf("%lld\n",ans);
	return 0;
}
