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

ans = 0
for i in range(min(n-1, k) + 1):
    com1 = fact[n] * fact_inv[i] * fact_inv[n-i] % mod
    com2 = fact[n-1] * fact_inv[i] * fact_inv[n-i-1] % mod
    mul = com1 * com2 % mod
    ans = (ans + mul) % mod

print(ans)