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>
typedef long long LL;
const int MAXN = 2e5 + 10;
const LL Mod = 1e9 + 7;
LL qpow(LL base, LL times)
{
	LL tmp = base % Mod;
	LL Ans = 1;
	while (times)
	{
		if (times & 1) Ans = Ans * tmp % Mod;
		times >>= 1;
		tmp = tmp * tmp % Mod;
	}
	return Ans % Mod;
}
LL nC[MAXN], n_1C[MAXN];
int main()
{
	LL n, k;
	std::cin >> n >> k;
	nC[0] = 1;
	for (LL i = 1; i <= n; i++)
	{
		LL cur = (nC[i - 1] * (n - i + 1)) % Mod;
		nC[i] = cur * qpow(i, Mod - 2) % Mod;
	}
	n_1C[0] = 1;
	for (LL i = 1; i < n; i++)
	{
		LL cur = (n_1C[i - 1] * (n - i)) % Mod;
		n_1C[i] = cur * qpow(i, Mod - 2) % Mod;
	}
	k = std::min(n, k);
	LL Ans = 0;
	for (int i = 0; i <= k; i++)
	{
		// std::cout<<"Ans is "<<Ans<<'\n';
		Ans = (Ans + ((nC[i] * n_1C[n - i - 1]) % Mod)) % Mod;
	}
	std::cout<<Ans<<'\n';
}