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    import sys\n    input = sys.stdin.readline\n\n    class TreiNode:\n        def __init__(self, char_num, depth):\n            self.end = False\n            self.child = [None] * char_num\n            self.depth = depth\n\n        def __setitem__(self, i, x):\n            self.child[i] = x\n\n        def __getitem__(self, i):\n            return self.child[i]\n\n    class Trei:\n        def __init__(self, char_num):\n            self.root = TreiNode(char_num, 0)\n            self.char_num = char_num\n\n        def add(self, S):\n            v = self.root\n            for s in S:\n                if v[s] is None:\n                    v[s] = TreiNode(self.char_num, v.depth + 1)\n                v = v[s]\n            v.end = True\n\n        def exist(self, S):\n            v = self.root\n            for s in S:\n                if v[s] is None:\n                    return False\n                v = v[s]\n            if v.end:\n                return True\n            else:\n                return False\n\n    N, L = list(map(int, input().split()))\n    T = Trei(2)\n    for _ in range(N):\n        S = input().rstrip('\\n')\n        S = [int(s) for s in S]\n        T.add(S)\n\n    g = 0\n    st = [T.root]\n    while st:\n        v = st.pop()\n        for i in range(2):\n            if v[i] is None:\n                d = L - v.depth\n                g ^= d & -d\n            else:\n                st.append(v[i])\n    if g:\n        print('Alice')\n    else:\n        print('Bob')\n\n\ndef __starting_point():\n    main()\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 20525