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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;


    void solve()
    {
        int N = cin.nextint;
        var L = cin.nextlong;

        var V = new List<Node>();
        V.Add(new Node(0));

        for (int i = 0; i < N; i++)
        {
            int now = 0;
            var S = ReadLine();
            for (int j = 0; j < S.Length; j++)
            {
                if (S[j] == '0')
                {
                    if (V[now].left == -1)
                    {
                        V[now].left = V.Count;
                        V.Add(new Node(j + 1));
                        now = V[now].left;
                    }
                    else
                    {
                        now = V[now].left;
                    }
                }
                else
                {
                    if (V[now].right == -1)
                    {
                        V[now].right = V.Count;
                        V.Add(new Node(j + 1));
                        now = V[now].right;
                    }
                    else
                    {
                        now = V[now].right;
                    }
                }
                if (j == S.Length - 1)
                {
                    V[now].exist = true;
                }
            }
        }
        long ans = 0;
        foreach (var u in V)
        {
            if (u.exist) continue;
            if (u.left == -1 || u.right == -1)
            {
                ans ^= (L - u.depth) & (u.depth - L);
            }
        }
        if (ans != 0)
        {
            WriteLine("Alice");
        }
        else
        {
            WriteLine("Bob");
        }
    }

}

class Node
{
    public int depth, left, right;
    public bool exist;
    public Node()
    {
        depth = left = right = -1;
        exist = false;
    }
    public Node(int d)
    {
        depth = left = right = -1;
        exist = false;
        depth = d;
    }
}
class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}