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

comb0 = [1] * (n)

for i in range(n-1):
    comb0[i + 1] = comb0[i] * (n - i) * pow(i + 1,mod - 2, mod) % mod

comb1 = [1] * (n)

for i in range(n-1):
    comb1[i + 1] = comb1[i] * (n - 1 - i) * pow(i + 1,mod - 2, mod) % mod

ans = 0

for i in range(min(n - 1, k) + 1):
    ans += comb0[i] * comb1[i]
    ans %= mod

print(ans)