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 = "N, L = map(int, input().split())\n\nmake = lambda:[None, None, 0]\nroot = make()\ndef construct(s):\n    n = root\n    for i in s:\n        if n[i] is None:\n            n[i] = n = make()\n        else:\n            n = n[i]\n    n[2] = 1\n\nfor i in range(N):\n    s = map(int, input())\n    construct(s)\n\ncaps = {}\nst = [(root, 0, 0)]\nwhile st:\n    n, i, l = st.pop()\n    if i:\n        if n[1] is None:\n            caps[L - l] = caps.get(L - l, 0) + 1\n        else:\n            if not n[1][2]:\n                st.append((n[1], 0, l+1))\n    else:\n        st.append((n, 1, l))\n        if n[0] is None:\n            caps[L - l] = caps.get(L - l, 0) + 1\n        else:\n            if not n[0][2]:\n                st.append((n[0], 0, l+1))\nans = 0\nfor v in caps:\n    k = caps[v]\n    if k % 2 == 0:\n        continue\n    v -= 1\n    r = 1\n    while v % 4 == 3:\n        v //= 4\n        r *= 4\n    if v % 4 == 1:\n        ans ^= r * 2\n    else:\n        ans ^= r\nprint('Alice' if ans else 'Bob')"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13609