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;
#define mod 1000000007
typedef long long ll;
ll modinv(ll a, ll p) {
    if (p == 1) return 0;
    ll pp = p, y = 0, x = 1;
    while (a > 1) {
        ll q = a / p, t = p;
        p = a % p, a = t, t = y, y = x - q * y, x = t;
    }
    if (x < 0) x += pp;
    return x;
}
int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n, k;
	cin >> n >> k;
	ll ans = 1;
	vector<ll> fra(n + 1, 1), inv(n + 1, 1);
	for (int i = 1; i <= n; i++) {
		fra[i] = fra[i - 1] * i % mod;
		inv[i] = modinv(fra[i], mod);
	}
	for (int i = 1; i <= min(n - 1, k); i++) {
		ll tmp = fra[n] * fra[n-1] % mod * inv[i] % mod * inv[i] % mod * inv[n - i] % mod * inv[n - i - 1] % mod;
		ans = (ans + tmp) % mod;
	}
	cout << ans << "\n";
	return 0;
}