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

fact = [1] * (2 * n + 1)
inv = [1] * (2 * n + 1)
invf = [1] * (2 * n + 1)
for i in range(2, 2 * n + 1):
  fact[i] = fact[i-1] * i % mod
  inv[i] = -inv[mod % i] * (mod // i) % mod
  invf[i] = invf[i-1] * inv[i] % mod

count = 0
for i in range(min(n, k+1)):
  c = fact[n] * invf[n-i] * invf[i] % mod
  count += c * fact[n-1] * invf[n-i-1] * invf[i] % mod
  count %= mod
print(count)