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 = list(map(int, input().split()))
mod = 1000000007
fac = [1]
inv = [1]
for i in range(n * 2):
    fac.append(fac[-1] * (i + 1) % mod)
    inv.append(pow(fac[-1], mod - 2, mod))


def cmb(n, k):
    if k < 0 or k > n:
        return 0
    return ((fac[n] * inv[k]) % mod * inv[n - k]) % mod


ret = 0
for m in range(min(k + 1, n)):
    ret = (ret + (cmb(n, m) * cmb(n - 1, n - m - 1)) % mod) % mod
print(ret)
