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 functools import cmp_to_key


def f(s, t):
    m = min(len(s), len(t))
    if s[:m] > t[:m]:
        return 1
    elif s[:m] < t[:m]:
        return -1
    else:
        if len(s) > len(t):
            return -1
        else:
            return 1


def ms(s, t):
    i = 0
    for c1, c2 in zip(s, t):
        if c1 != c2:
            return i
        i += 1
    return i


def xxor(x):
    if x & 3 == 0:
        return x
    if x & 3 == 1:
        return 1
    if x & 3 == 2:
        return x + 1
    if x & 3 == 3:
        return 0


def gray(x):
    return x ^ (x // 2)


n, l = map(int, input().split())
s = [input() for _ in range(n)]
s.sort(key=cmp_to_key(f))
g = gray(l) ^ gray(l - len(s[0]))
for i in range(n - 1):
    b = ms(s[i], s[i + 1]) + 1
    g ^= gray(l - b + 1) ^ gray(l - b)
    t = len(s[i + 1]) - b
    g ^= gray(l - b) ^ gray(l - b - t)
if g == 0:
    print('Bob')
else:
    print('Alice')