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;
typedef long long ll;
const int mod=1e9+7;

ll n,k;
const int maxn=2e5+5;
ll x[maxn][2];
ll fast_pow(ll a, ll b){
	ll ret = 1;
	for(;b;b>>=1){
		if(b&1) ret = ret * a % mod;
		a = a * a % mod;
	}
	return ret;
}

int main(){
	cin >> n >> k;
	ll mns=1;
	x[0][0]=1;
	x[0][1]=1;
	for (int i=1;i<=n-1;i++){
		mns *= (n+1-i);
		mns %= mod;
		mns *= fast_pow(i,mod-2);
		mns %= mod;	
		x[i][0]=mns;
	}
	mns = 1;
	for (int i=1;i<=n-1;i++){
		mns *= (n-i);
		mns %= mod;
		mns *= fast_pow(i,mod-2);
		mns %= mod;	
		x[i][1]=mns;
	}
	ll s=0;
	for (int i=0;i<=min(n-1,k);i++){
		s += x[i][0]*x[i][1];	
		s %= mod;
	}
	while (s<0) s+=mod;
	cout << s;
	return 0;
}
