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
def main():

    n, k = map(int, input().split())
    mod = pow(10, 9) + 7

    g1 = [1, 1]
    g2 = [1, 1]
    inv = [0, 1]

    for i in range(2, n+1):
        g1.append((g1[-1] * i) % mod)
        inv.append( ( -inv[mod % i] * (mod//i)) % mod )
        g2.append((g2[-1] * inv[-1]) % mod)

    def combi(n, r):
        r = min(r, n-r)
        return g1[n]*g2[r]*g2[n-r]%mod

    if k >= n-1:
        k = n-1
    ans = 1
    for i in range(1, k+1):
        ans += (combi(n, i) * combi(n-1, n-i-1)) % mod
    return ans % mod


if __name__ == '__main__':
    print(main())