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 random\nN, L = list(map(int,input().split()))\nM = 2*10**5+1\nsets = [set() for _ in range(M+1)]\n\nMOD = 282525872416376072492401\nr_max = 10**6\ninv_t = [0,1]\nfor i in range(2,r_max+1):\n  #print(MOD % i)\n  inv_t.append(inv_t[MOD % i] * (MOD - MOD // i) % MOD)\nr = random.randint(10**5, r_max)\nrinv = inv_t[r]\n#print(r, rinv)\n\ndef has(s):\n  ans = 0\n  i = 0\n  for x in s:\n    ans *= r\n    ans += int(x) + (i+1)**2\n    ans %= MOD\n    i += 1\n  return ans % MOD\ndef tract(x, s, l):\n  return ((x - int(s) - l**2) * rinv ) %MOD\n \nstrs = []\ndic = {}\nct = 0\nfor i in range(N):\n  s = input()\n  strs.append(s)\n  sets[len(s)].add(has(s))\n  if has(s) in dic:\n    print(("warning!!", s))\n    ct += 1\n  dic[has(s)] = i\n#print(ct)\n#print(sets[0:3])\n#print(dic)\nfree_num = [0 for _ in range(M+1)]\nfor l in range(M,0,-1):\n  while len(sets[l]) > 0:\n    x = sets[l].pop()\n    #print(x, dic[x], strs[dic[x]], l)\n    #if l-1 > len(strs[dic[x]]):\n      #print(l-1, x, dic[x], strs[dic[x]], sets[l])\n    last = strs[dic[x]][l-1]\n    x_p = tract(x, last, l)\n    sets[l-1].add(x_p) \n    dic[x_p] = dic[x]\n    x_anti = (x_p*r + 1-int(last) + l**2) % MOD\n    if x_anti in sets[l]:\n      sets[l].remove(x_anti)\n    else:\n      free_num[l] += 1\n    #print(l, x, free_num[0:2],sets[0:3], x_p, x_anti, last)\n#print(free_num[0:100])\nGrandy = 0\nfor i in range(M+1):\n  G_base = L - i + 1\n  if free_num[i] % 2 == 1:\n    #print(i, G_base)\n    Grandy ^= (G_base & -G_base)\n#print(Grandy)    \nprint(("Alice" if Grandy > 0 else "Bob"))\n  \n#print(2**54 & -2**54, 2**54) \n  \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 90906353