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, 1]
finv = [1, 1]
inv = [0, 1]
def COMinit():
  #N_C_kのN
  for i in range(2, n+10):
    fac.append(fac[-1]*i%Mod)
    inv.append((-inv[Mod%i] * (Mod//i)) % Mod)
    finv.append(finv[-1] * inv[-1] % Mod)


def COM(n, k):
  if n < 0 or k < 0 or n < k:
    return 0
  return fac[n] * (finv[k] * finv[n-k] % Mod) % Mod


COMinit()
ans = 0
for i in range(min(n, k)+1):
  tmp = COM(n, i) % Mod
  tmp *= COM(i+n-i-1, i)
  tmp %= Mod
  ans += tmp
  ans %= Mod
print(ans)