Problem:
Score : 700 points

Problem Statement

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 1

2 2
00
01

Sample Output 1

Alice

If Alice adds 1, Bob will be unable to add a new string.

Sample Input 2

2 2
00
11

Sample Output 2

Bob

There are two strings that Alice can add on the first turn: 01 and 10.
In case she adds 01, if Bob add 10, she will be unable to add a new string.
Also, in case she adds 10, if Bob add 01, she will be unable to add a new string.

Sample Input 3

3 3
0
10
110

Sample Output 3

Alice

If Alice adds 111, Bob will be unable to add a new string.

Sample Input 4

2 1
0
1

Sample Output 4

Bob

Alice is unable to add a new string on the first turn.

Sample Input 5

1 2
11

Sample Output 5

Alice

Sample Input 6

2 3
101
11

Sample Output 6

Bob

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

#!/usr/bin/env python3
import heapq

def solve(n, l, s):

    heapq.heapify(s)

    r = 0
    while len(s):
        li, si = heapq.heappop(s)
        lp = li + 1
        sp = si[:-1]
        if len(s):
            lj, sj = heapq.heappop(s)
            if lj != li or sj[:-1] != sp:
                heapq.heappush(s, (lj, sj))
                r ^= (l + li) % 2 + 1
            if lp != 0:
                heapq.heappush(s, (lp, sp))
        else:
            r ^= (l + li) % 2 + 1
            break


    return r


def main():
    n, l = input().split()
    n = int(n)
    l = int(l)
    s = []
    for _ in range(n):
        si = input()
        s.append((-len(si), si))

    print('Alice' if solve(n, l, s) else 'Bob')


if __name__ == '__main__':
    main()