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 main():\n    N,L = map(int,input().split())\n    keys = []\n    grundy_num=0\n    if N==1:\n        print("Alice")\n        return\n    for i in range(N):\n        s = input()\n        #merge node:\n        while len(s)>0:\n            if s[-1]==\'1\' and s[:-1]+\'0\' in keys:\n                keys.remove(s[:-1]+\'0\')\n                s = s[:-1]\n            elif s[-1]==\'0\' and s[:-1]+\'1\' in keys:\n                keys.remove(s[:-1]+\'1\')\n                s = s[:-1]\n            else:\n                if s!="":\n                    keys.append(s)\n                break\n    if len(keys):\n        keys = sorted(keys,key=len,reverse=True)\n        grundy_list = []\n        while len(keys):\n            j = keys[0]\n            keys.remove(j)\n            temp_s = list(reversed(bin(L-len(j)+1)))\n            grundy_list.append(1 << temp_s.index(\'1\'))\n            if j[:-1]!="":\n                keys.append(j[:-1])\n            j = j[:-1]\n            #merge node\n            while len(j)>0:\n                if j[-1]==\'1\' and j[:-1]+\'0\' in keys:\n                    keys.remove(j[:-1]+\'0\')\n                    keys.remove(j)\n                    j = j[:-1]\n                    if j!="":\n                        keys.append(j)\n                elif j[-1]==\'0\' and j[:-1]+\'1\' in keys:\n                    keys.remove(j[:-1]+\'1\')\n                    keys.remove(j)\n                    j = j[:-1]\n                    if j!="":\n                        keys.append(j)\n                else:\n                    break\n            keys = sorted(keys,key=len,reverse=True)\n        grundy_num = grundy_list[0]\n        for i in range(1,len(grundy_list)):\n            grundy_num = grundy_num^grundy_list[i]\n    print("Bob" if grundy_num==0 else "Alice")\n\n\ndef __starting_point():\n    main()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15409