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
def prepare(m, mod=10 ** 9 + 7):
	fac = [1] * (m + 1)
	inv = [1] * (m + 1)
	for i in range(1, m + 1):
		fac[i] = fac[i - 1] * i % mod
	inv[-1] = pow(fac[-1], mod - 2, mod)
	for i in range(m - 1, -1, -1):
		inv[i] = inv[i + 1] * (i + 1) % mod
	return fac, inv

n, k = map(int, input().split())
mod = 10 ** 9 + 7
fac, inv = prepare(n)

def cmb(n, r):
	assert n >= r >= 0
	return fac[n] * inv[n - r] * inv[r] % mod

ans = 0
for i in range(min(n, k + 1)):
	ans += cmb(n, i) * cmb(n - 1, i)
	ans %= mod
print(ans % mod)