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
from collections import defaultdict


def mod_inv(a, m):
    return pow(a, m-2, m)


def combination(a, b):
    if b > a - b:
        return combination(a, a - b)
    ans = fact[a] * ifact[b] * ifact[a-b]
    return ans


MOD = 10**9+7
n, k = map(int, input().split())
k = min(k, n-1)

fact = defaultdict(int)
fact[0] = 1
ifact = defaultdict(int)
ifact[0] = 1
for i in range(1, n+1):
    fact[i] = fact[i-1] * i
    fact[i] %= MOD
    ifact[i] = mod_inv(fact[i], MOD)
    ifact[i] %= MOD

ans = 0
for i in range(k+1):
    ans += combination(n, i) * combination((n-i-1)+i, i)
    ans %= MOD

print(ans % MOD)


