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
import sys
from functools import lru_cache

sys.setrecursionlimit(10 ** 7)

MOD = 10 ** 9 + 7

@lru_cache(None)
def combination(n, k):
    if k == 0:
        return 1
    else:
        return ((combination(n, k-1) * (n-k+1) % MOD) * pow(k, MOD-2, MOD)) % MOD

n, k = map(int, input().split())

s = 0
for m in range(0, min(k+1, n)):
    s += combination(n, min(m, n - m)) * combination(n - 1, min(m, n - m - 1))
    s %= MOD

print(s)