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())
D = 10**9 + 7

up = [1] * (n + 1)
down = [0] * (n + 1)
for i in range(1, n + 1):
  up[i] = (up[i - 1] * i) % D
down[n] = pow(up[n], D - 2, D)
for i in range(n, 0, -1):
  down[i - 1] = (down[i] * i) % D
  
def cmd(n, r, D):
  if r < 0 or r > n:
    return 0
  else:
    return (up[n] * down[r] * down[n - r]) % D

A = 0
k = min(k, n-1)
t = 0
while t <=k:
  A = (A + cmd(n-1, t, D) * cmd(n, t, D)) % D
  t = t+1
print (A)