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
mo = 10 ** 9 + 7
n, k = map(int, input().split())
def rev(u):
    return pow(u, mo - 2, mo)
def C(p, q):
    ans = 1
    for i in range(q):
        ans = ans * (p - i) % mo
    for i in range(q):
        ans = ans * rev(i + 1) % mo
    return (ans + mo) % mo
if k >= n - 1:
    print(C(2 * n - 1, n))
    exit()
u, v = 1, 1
ans = 1
for i in range(k):
    u = u * (n - 1 - i) * rev(i + 1) % mo
    v = v * (n - i) * rev(i + 1) % mo
    ans = (ans + u * v) % mo
print(ans)