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())
k = min(k, n - 1)
p = 10 ** 9 + 7
size = n + 100
f_list = [1] * size
if_list = [1] * size
for i in range(1, size):
    f_list[i] = (f_list[i - 1] * i) % p
    if_list[i] = pow(f_list[i], p-2, p)

def cmb(n, r):
    return f_list[n] * if_list[r] * if_list[n-r] % p

# 初期値は0人の部屋が0個の場合
ans = 1
for i in range(1, k + 1):
    ans += cmb(n, i) * cmb(n - 1, i)
    ans = ans % p
print(ans)