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:
import sys
sys.setrecursionlimit(2 * 10 ** 5)


class TrieNode:
    def __init__(self, char):
        self.char = char
        self.nextnode = dict()
        self.is_indict = False


class Trie:
    def __init__(self, charset):
        self.charset = charset
        self.root = TrieNode('')

    def add(self, a_str):
        node = self.root
        for i, char in enumerate(a_str):
            if char not in node.nextnode:
                node.nextnode[char] = TrieNode(char)
            node = node.nextnode[char]
            if i == len(a_str) - 1:
                node.is_indict = True

    def dfs(self, node, dep):
        ret, cnt = 0, 0
        if node.is_indict:
            return 0
        for s in '01':
            if s not in node.nextnode:
                cnt += 1
            else:
                ret ^= self.dfs(node.nextnode[s], dep + 1)
        height = L - dep
        if cnt % 2:
            power2 = 0
            while height > 0 and height % 2 == 0:
                power2 += 1
                height //= 2
            ret ^= 2 ** power2
        return ret

    def debug_output(self, node, now):
        print(node.char, list(node.nextnode.items()), node.is_indict, now)
        if node.is_indict:
            print(now)
        for n in node.nextnode.values():
            self.debug_output(n, now + n.char)

N, L = map(int, input().split())
T = Trie('01')
for _ in range(N):
    T.add(input())
# T.debug_output(T.root, '')
print("Alice" if T.dfs(T.root, 0) else "Bob")