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\n#from collections import defaultdict\nsys.setrecursionlimit(10**6)\n\ndef input():\n\treturn sys.stdin.readline()[:-1]\nn, l = list(map(int, input().split()))\nss = [list(input())[::-1] for _ in range(n)]\n\ndef addTree(tree, sentence):\n\tif not sentence:\n\t\treturn None   \n\n\tif sentence[-1] not in tree:\n\t\ttree[sentence[-1]] = {}\n\n\tp = sentence.pop()\n\ttree[p] = addTree(tree[p], sentence)\n\n\treturn tree\n\ndef createTree(sentences):    \n\ttree = {}\n\tfor sentence in sentences:\n\t\ttree = addTree(tree, sentence)\n\n\treturn tree\n\ntree = createTree(ss)\n#print(tree)\n\ngrundy = 0\ndef dfs(cur, level):\n\tnonlocal grundy\n\tif cur is None:\n\t\treturn\n\telif len(cur) == 1:\n\t\tgrundy ^= (l-level) & (-l+level)\n\tfor k in list(cur.keys()):\n\t\tdfs(cur[k], level+1)\n\treturn\n\t\ndfs(tree, 0)\n\nif grundy == 0:\n\tprint("Bob")\nelse:\n\tprint("Alice")\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: