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.

-----Sample Input-----
2 2
00
01

-----Sample Output-----
Alice

If Alice adds 1, Bob will be unable to add a new string.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "def getGrundyNumber(x):\n    ans = 1\n    while x % (ans * 2) == 0:\n        ans *= 2\n    return ans\n\n\nN, L = list(map(int, input().split()))\nSs = [input() for i in range(N)]\n\n# トライ木を作成する\nTrie = [[-1, -1]]\nfor S in Ss:\n    iT = 0\n    for c in map(int, S):\n        if Trie[iT][c] == -1:\n            Trie += [[-1, -1]]\n            Trie[iT][c] = len(Trie) - 1\n        iT = Trie[iT][c]\n\n# 子が１つの頂点を探す\nHgts = {}\nstack = [(0, L + 1)]\nwhile stack:\n    iT, Hgt = stack.pop()\n    num = 0\n    for c in Trie[iT]:\n        if c != -1:\n            stack.append((c, Hgt - 1))\n            num += 1\n\n    if num == 1:\n        Hgts[Hgt - 1] = Hgts.get(Hgt - 1, 0) + 1\n\n# Grundy数のXORを求める\nans = 0\nfor Hgt, num in list(Hgts.items()):\n    if num % 2:\n        ans ^= getGrundyNumber(Hgt)\n\nif ans:\n    print('Alice')\nelse:\n    print('Bob')\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13629