Problem: For strings s and t, we will say that s and t are prefix-free when neither is a prefix of the other.

Let L be a positive integer. A set of strings S is a good string set when the following conditions hold true:

* Each string in S has a length between 1 and L (inclusive) and consists of the characters `0` and `1`.
* Any two distinct strings in S are prefix-free.



We have a good string set S = \\{ s_1, s_2, ..., s_N \\}. Alice and Bob will play a game against each other. They will alternately perform the following operation, starting from Alice:

* Add a new string to S. After addition, S must still be a good string set.



The first player who becomes unable to perform the operation loses the game. Determine the winner of the game when both players play optimally.

Constraints

* 1 \leq N \leq 10^5
* 1 \leq L \leq 10^{18}
* s_1, s_2, ..., s_N are all distinct.
* { s_1, s_2, ..., s_N } is a good string set.
* |s_1| + |s_2| + ... + |s_N| \leq 10^5

Input

Input is given from Standard Input in the following format:


N L
s_1
s_2
:
s_N


Output

If Alice will win, print `Alice`; if Bob will win, print `Bob`.

Examples

Input

2 2
00
01


Output

Alice


Input

2 2
00
11


Output

Bob


Input

3 3
0
10
110


Output

Alice


Input

2 1
0
1


Output

Bob


Input

1 2
11


Output

Alice


Input

2 3
101
11


Output

Bob

Solution (in PYTHON3):

Solution:
from collections import defaultdict


def solve(n, l, nums):
    xor = 0

    if n == 1:
        for i in range(min(nums), l + 1):
            xor ^= i & -i
        return xor

    for i in range(min(nums), l + 1):
        ni = nums[i]
        for k in ni:
            if k ^ 1 not in ni:
                xor ^= i & -i
            nums[i + 1].add(k // 2)
        del nums[i]
    return xor


n, l = map(int, input().split())
nums = defaultdict(set)
for s in (input() for _ in range(n)):
    nums[l - len(s) + 1].add(int(s, 2) + (1 << len(s)))

print('Alice' if solve(n, l, nums) else 'Bob')