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

K = min(K, N - 1)

fact = [1]
facinv = [1]
for i in range(1, N + 1):
    fact.append(fact[-1]*i % mod)


def nCr(n, r):
    num = fact[n]
    div = fact[r] * fact[n - r] % mod
    return num * pow(div, mod - 2, mod) % mod


move = [0] * (N + 1)
move[0] = 1
for i in range(1, N + 1):
    x = nCr(N, i) * nCr(N - 1, N - i - 1) % mod
    move[i] = x

for i in range(1, N):
    move[i] = (move[i - 1] + move[i]) % mod

ans = move[K]
print(ans)
