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:
class Node():
    def __init__(self):
        self.lt = None
        self.rt = None
        self.dep = None

class Trie():
    def __init__(self):
        self.root = Node()
        self.root.dep = 0

    def add(self, string):
        node = self.root
        for s in string:
            if s == '0':
                if node.lt is None:
                    node.lt = Node()
                    node.lt.dep = node.dep + 1
                node = node.lt
            else:
                if node.rt is None:
                    node.rt = Node()
                    node.rt.dep = node.dep + 1
                node = node.rt

N, L = map(int, input().split())

trie = Trie()

for _ in range(N):
    s = input()
    trie.add(s)

subgame = []
stack = [trie.root]

while stack:
    node = stack.pop()
    if node.lt is None and node.rt is None:
        continue
    elif node.rt is None:
        stack.append(node.lt)
        subgame.append(L - node.dep)
    elif node.lt is None:
        stack.append(node.rt)
        subgame.append(L - node.dep)
    else:
        stack.append(node.lt)
        stack.append(node.rt)

def grundy(n):
    if n == 0: return 0
    if n % 2 == 1: return 1
    if n == 2**(n.bit_length() - 1):
        return n
    return grundy(n - 2**(n.bit_length() - 1))

g = 0

for l in subgame:
    g ^= grundy(l)

print('Alice' if g != 0 else 'Bob')