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

factorial = [1]
inverse = [1]
for i in range(1, 2*n):
    factorial.append(factorial[-1] * i % mod)
    inverse.append(pow(factorial[-1], mod - 2, mod))

def comb(n, r, mod):
    if n < r or r < 0:
        return 0
    elif r == 0:
        return 1
    return factorial[n] * inverse[r] * inverse[n - r] % mod


if k >= n-1:
    print(comb(2*n-1, n-1, mod))
else:
    sikiri = n - 1
    basho = 2 * n - 1
    ans = 0
    for i in range(k+1):
        ans = (ans + comb(n, i, mod) * comb(sikiri, sikiri-i, mod)) % mod
    print(ans)