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
n,k = map(int,input().split())
k = min(k,n-1)
mod = 10**9 + 7
ans = 1
z0 = 1
z1 = 1
def inv(x):
  y = 1
  while x != 1:
    y *= mod // x + 1
    y %= mod
    x -= mod % x
  return y
for i in range(k):
  z0 *= n-i
  z0 %= mod
  z0 *= inv(i+1)
  z0 %= mod
  z1 *= n-1-i
  z1 %= mod
  z1 *= inv(i+1)
  z1 %= mod
  ans += z0 * z1
  #print(z0,z1,z0*z1,ans)
  ans %= mod
print(ans)