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\nfrom collections import deque\n\nsys.setrecursionlimit(10000)\nINF = float(\'inf\')\n\nN, L = list(map(int, input().split()))\nS = set()\nfor _ in range(N):\n    S.add(input())\n\n\n# 追加できるのが 01... だけで\n# L が 4 とすると\n# 01: 次はない\n# 010: 011 がある\n# 011: 010 がある\n# 0100: 011, 0101 がある\n# 0101: 011, 0100\n# 0110: 010, 0111\n# 0111: 010, 0110\n# 候補の長さと L だけによって次の候補の長さと数が決まる\ndef grundy(size):\n    """\n    :param int size: 候補の長さ\n    :return:\n    """\n    # gs = {0}\n    # g = 0\n    # for sz in range(size + 1, L + 1):\n    #     g ^= grundy(sz)\n    #     gs.add(g)\n    #\n    # i = 0\n    # while i in gs:\n    #     i += 1\n    # return i\n    i = 1\n    while (L - size + 1) % i == 0:\n        i *= 2\n    return i // 2\n\n\n# S の各要素からトライ木つくる\ntrie = {}\nfor s in S:\n    t = trie\n    for c in s:\n        if c not in t:\n            t[c] = {}\n        t = t[c]\n\n# 候補文字列の長さのリスト\nok_size_list = []\nchildren = deque()\nchildren.append((trie, 0))\nwhile len(children) > 0:\n    node, size = children.popleft()\n    # 0 か 1 か片方しか行けなかったら、行けない方は S の prefix にならない\n    # 両方行けない場合はどう追加しても S のいずれかが prefix になってしまうからダメ\n    if len(node) == 1:\n        ok_size_list.append(size + 1)\n    for c, child in node.items():\n        children.append((child, size + 1))\n\ng = 0\nfor size in ok_size_list:\n    g ^= grundy(size)\nif g != 0:\n    print(\'Alice\')\nelse:\n    print(\'Bob\')'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14097