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

fact = [0] * (n+1)
inv_fact = [0] * (n+1)

fact[0] = 1
for i in range(1, n+1):
    fact[i] = fact[i-1] * i % MOD

inv_fact[n] = pow(fact[n], MOD-2, MOD)
for i in range(n, 0, -1):
    inv_fact[i-1] = inv_fact[i] * i % MOD


def nCk(n, k):
    return fact[n] * inv_fact[k] * inv_fact[n-k] % MOD
  
ans = 1
for i in range(1, n):
    if i > k:
      break
    ans += nCk(n, i) * nCk(n-1, n-i-1) % MOD
print(ans % MOD)