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 <iostream>
#include <cstdio>
#define N 200005
using namespace std;

typedef long long ll;
ll M = 1e9 + 7;
ll n, k, s, fac[N] = {1, 1}, inv[N] = {1, 1}, fiv[N] = {1, 1};

ll C(ll p, ll q) {
	if (p < q) return 0;
	return fac[p] * fiv[q] % M * fiv[p - q] % M;
}

ll H(ll p, ll q) {
	return C(p + q - 1, q);
}

int main()
{
	ll i;
	cin >> n >> k;
	for (i = 2; i <= n; i++) {
		fac[i] = fac[i - 1] * i % M;
		inv[i] = inv[M % i] * (M - M / i) % M;
		fiv[i] = fiv[i - 1] * inv[i] % M;
	}
	for (i = 0; i <= min(n, k); i++) {
		s = (s + C(n, i) * H(n - i, i)) % M;
	}
    cout << s << endl;
    return 0;
}