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 MAXN 200010
#define ll long long
#define mod 1000000007

using namespace std;

int n, sum = 1, k;

ll a[MAXN], fac[MAXN];

int qp(int x, int y) {
	ll res = 1, base = x;
	while (y) {
		if (y & 1) {
			res = (res * base) % mod;
		}
		base = (base * base) % mod;
		y >>= 1;
	}
	return res;
}

ll F(int x, int y) {
	if (y > x) return 0;
	return ((fac[x] * a[y]) % mod) * a[x - y] % mod;
}

int main() {
	cin >> n >> k;
	a[0] = 1;
	fac[0] = 1;
	for (int i = 1; i <= n; i++) {
		fac[i] = (ll)(fac[i - 1] * i) % mod;
		a[i] = qp(fac[i], mod - 2);
	}
	for (ll i = 1; i <= min(n - 1, k); i++) {
		ll ssum = F(n, i);
		ll t = n - i, u = F(n - 1, n - t);
		sum = (sum + ssum * u % mod) % mod;
	}
	cout << sum << endl;
	return 0;
} 