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
# min(n-1,k)以下の自然数mに対してnCm*n-1Cn-m-1の和を求める
n, k = map(int, input().split())
p = 10 ** 9 + 7
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]

for i in range(2, 2 * 10 ** 5 + 1):
    g1.append((g1[-1] * i) % p)
    inverse.append((-inverse[p % i] * (p // i)) % p)
    g2.append((g2[-1] * inverse[-1]) % p)


def cmb(n, r):
    return g1[n] * g2[r] * g2[n - r] % p


ans = 0
for m in range(min(n - 1, k) + 1):
    ans += cmb(n, m) * cmb(n - 1, n - m - 1) % p
print(ans % p)
