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
// In the name of God

#include <bits/stdc++.h>

using namespace std;

#define int long long

const int mod = 1e9+7;
const int N = 2e5+5;

int fac[N];

int fast_pw(int x, int y) {
	int ret = 1;
	for(;y;y>>=1) {
		if(y&1) ret=(ret*x)%mod;	
		x=(x*x)%mod;
	}
	return ret;
}

int comb(int n, int k) {
	int ans = fac[n];
	int a1 = fast_pw(fac[k], mod-2);
	int a2 = fast_pw(fac[n-k], mod-2);
	ans = (ans*a1)%mod;
	ans = (ans*a2)%mod;
	return ans;
}

signed main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	fac[0] = 1;
	for(int i=1;i<N;i++) fac[i]=(fac[i-1]*i)%mod;
	int n, k;
	cin >> n >> k;
	int ans = 1;
	k=min(k, n-1);
	for(int i=1;i<=k;i++) {
		ans += comb(n, i)*comb(n-1, n-i-1);
		ans %= mod;
	}
	cout << ans;
	return 0;
}
