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
n = N * 2
fact = [1]*(n+1)
rfact = [1]*(n+1)
r = 1
for i in range(1, n+1):
  fact[i] = r = r * i % mod
rfact[n] = r = pow(fact[n], mod-2, mod)
for i in range(n, 0, -1):
  rfact[i-1] = r = r * i % mod
def comb(n, k):
  return fact[n] * rfact[k] * rfact[n-k] % mod

if N <= K+1:
  print(comb(n-1,N))
else:
  ans = (1 + (N * (N-1))) % mod
  for i in range(2,K+1):
    mini_ans = (comb(N,i) * comb(N-1,N-i-1)) % mod
    ans = (ans + mini_ans) % mod
  print(ans)