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
MOD = 10 ** 9 + 7
fac = [1] * (5 * 10 ** 5 + 1)
for i in range(len(fac) - 1):
    fac[i + 1] = fac[i] * (i + 1) % MOD


n, k = map(int, input().split())
if k >= n:
    print(fac[2 * n] * pow(2, MOD - 2, MOD) *
          pow(fac[n], MOD - 2, MOD) ** 2 % MOD)
else:
    ans = 0
    for i in range(k + 1):
        ans += fac[n - 1] * pow(fac[i], MOD - 2, MOD) * \
            pow(fac[n - i - 1], MOD - 2, MOD) * fac[n] * pow(fac[n - i],
                                                             MOD - 2, MOD) * pow(fac[i], MOD - 2, MOD) % MOD
    print(ans % MOD)
