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 maxn=4e5+10;
const int mod=1e9+7;
ll fac[maxn],inv[maxn];
void gcd(ll a,ll b,ll &d,ll &x, ll &y){
	if(b){
		gcd(b,a%b,d,y,x); y-=x*(a/b);
	}
	else {
		d=a,x=1,y=0;
	}
}
void init(){
	fac[0]=fac[1]=1;
	for(int i=2;i<maxn;i++)
		fac[i]=fac[i-1]*i%mod;
}
ll c(ll n,ll k){
	ll x,y,d;
	ll tmp=(fac[k]*fac[n-k])%mod;
	gcd(tmp,mod,d,x,y);
	y=fac[n]*(x%mod)%mod;
	if(y<0) y+=mod;
	return y;
}
int main(){
	ll n,k;
	init();
	cin>>n>>k;
	ll ans=c(2*n-1,n);
	if(k>=n-1){
		//cout<<0;
		cout<<ans; return 0; 
	}
	else {
		for(int i=1;i<n-k;i++){
			ans-=c(n,i)*c(n-1,i-1)%mod;
			ans+=mod;
			ans%=mod;
		}
		cout<<ans;
	}
} 