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
mod = 10 ** 9 + 7
n, k = map(int, input().split())
binomial = [1]
cum = 1
for i in range(1, n + 2):
    cum *= i
    cum = cum % mod
    binomial.append(cum)
inv = []
tmp = pow(cum, mod - 2, mod)
inv.append(tmp)
for j in range(n + 1, 0, -1):
    tmp = j * tmp % mod
    inv.append(tmp)
inv.reverse()

def comb(n, k):
    return binomial[n] * inv[n - k] % mod * inv[k] % mod if n >= k else 0
k = min(k, n - 1)
ans = 0
for m in range(k + 1):
        tmp = comb(n, m) * binomial[n - 1] * inv[n - 1 - m] * inv[m]
        ans += tmp % mod
ans %= mod
print(ans)