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())

mod = 10 ** 9 + 7

fac = [1]
for i in range(1, 2 * n + 1) :
  fac.append(fac[-1] * i % mod)
inv = [pow(fac[-1], mod - 2, mod)]
for i in range(2 * n, 0, -1) :
  inv.append(inv[-1] * i % mod)
  
inv = inv[::-1]

def comb(n, r) :
  if n < 1 or n < r : return 0
  return fac[n] * inv[r] * inv[n-r] % mod
  
ret = comb(n + n - 1, n)
for i in range(1, n - k) :
  ret -= comb(n - 1, k + i) * comb(n, k + i)
  ret %= mod
print(ret % mod)