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;
using ll=long long;
constexpr char sp=' ';
constexpr ll mod=1000000007;

int N,K;
ll f[200001],res;

ll pw(ll x,int y){
	ll a=1;
	while(y){
		if(y&1)a=a*x%mod;
		x=x*x%mod;
		y/=2;
	}
	return a;
}
 
ll modinv(ll x){
	return pw(x,mod-2);
}

ll comb(int n,int r){
	return f[n]*modinv(f[n-r]*f[r]%mod)%mod;
}

int main(){
	cin>>N>>K;
	K=min(K,N-1);
	f[0]=1;
	for(ll i=1;i<=200000;i++){
		f[i]=f[i-1]*i%mod;
	}
	for(int i=0;i<=K;i++){
		res+=comb(N,i)*comb(N-1,i);
		res%=mod;
	}
	cout<<res<<endl;
}
