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(n - 1, k)

mod = 10 ** 9 + 7
fact = [1] * (n + 1)
ifact = [1] * (n + 1)

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


def comb(x, y):
    if y < 0 or y > x:
        return 0
    return (fact[x] * ifact[x - y] * ifact[y]) % mod


ans = 0
for i in range(k + 1):
    ans += comb(n, i) * comb(n - 1, n - i - 1) % mod
    ans %= mod
print(ans)
