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 = "import sys\ninput = sys.stdin.readline\nsys.setrecursionlimit(10**6)\nfrom collections import deque\n\nN,M = map(int,input().split())\nwords = [deque(input().rstrip()) for _ in range(N)]\n\n# 深さLのfull treeの小さい方を計算してみる\ndef G_small():\n    G = [0] * 100\n    G_cum = [0] * 100\n    G[0] = 1\n    G_cum[0] = 1\n    for n in range(1,100):\n        can_make = set(G_cum[n-1]^G_cum[x] for x in range(n)) | set([G_cum[n-1]])\n        rest = set(range(n+10)) - can_make\n        G[n] = min(rest)\n        G_cum[n] = G_cum[n-1] ^ G[n]\n    return G\n\n# print([(n,G[n]) for n in range(100)])\n# G[n] = 2**ord_2(n+1)\n# 値がわかれば証明は易しい\n\ndef G(n):\n    n += 1\n    x = 1\n    while not n & 1:\n        n >>= 1\n        x <<= 1\n    return x\n\ndef calc_grandy(words,L):\n    if not words:\n        return G(L)\n    if len(words) == 1 and words[0] == deque():\n        return 0\n    words_0 = []\n    words_1 = []\n    for word in words:\n        first = word.popleft()\n        if first == '0':\n            words_0.append(word)\n        else:\n            words_1.append(word)\n    return calc_grandy(words_0,L-1) ^ calc_grandy(words_1,L-1)\n\ng = calc_grandy(words,M)\n\nanswer = 'Alice' if g != 0 else 'Bob'\nprint(answer)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13605