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:
# nimber: 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 32, ...

class Node:
    def __init__(self, size, avail):
        self.end = False
        self.nxt = [None] * size
        self.avail = avail
    def __setitem__(self, i, x): self.nxt[i] = x
    def __getitem__(self, i): return self.nxt[i]

def makeTrie(strs, size):
    root = Node(size, l)
    for s in strs:
        n = root
        for c in s:
            i = int(c) # Change this to adapt. ex: ord(c)-ord("A")
            if not n[i]: n[i] = Node(size, n.avail-1)
            n = n[i]
        n.end = True
    return root

def nimber(n):
    x = 1
    while n%2 == 0: n//= 2; x*= 2
    return x

input = __import__('sys').stdin.readline
n, l = map(int,input().split())
strs = [input().rstrip() for i in range(n)]
T = makeTrie(strs, 2)

ans = 0
stack = [T]
while stack:
    n = stack.pop()
    for i in 0, 1:
        if not n[i]: ans^= nimber(n.avail)
        elif not n[i].end: stack.append(n[i])
print("Alice" if ans else "Bob")