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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		Array.Sort(S,(a,b) => a.Length.CompareTo(b.Length));
		
		var H0 = new HashSet<String>();
		for(int m=1;m<=Math.Min(L,20);m++){
			var H = new HashSet<String>();
			for(int i=0;i<(1<<m);i++){
				var ca = new char[m];
				for(int j=0;j<m;j++){
					ca[j] = ((i >> j) & 1) == 0 ? '0' : '1';
				}
				bool chk = true;
				foreach(var s in H0){
					int l = Math.Min(s.Length, m);
					bool chk2 = true;
					for(int k=0;k<l;k++){
						chk2 &= s[k] == ca[k];
					}
					if(chk2){
						chk = false;
						break;
					}
				}
//Console.WriteLine("{0} {1}",new String(ca),chk);
				if(!chk) continue;
				foreach(var s in S){
					int l = Math.Min(s.Length, m);
					bool chk2 = true;
					for(int k=0;k<l;k++){
						chk2 &= s[k] == ca[k];
					}
					if(chk2){
						chk = false;
						break;
					}
				}
//Console.WriteLine("{0} {1}",new String(ca),chk);
				if(chk) H.Add(new String(ca));
			}
			foreach(var s in H) H0.Add(s);
		}
//foreach(var s in H0) Console.WriteLine(s);
		Console.WriteLine(H0.Count % 2 == 0 ? "Bob" : "Alice");
		
	}
	int N;
	long L;
	String[] S;
	public Sol(){
		var d = rla();
		N = (int) d[0]; L = d[1];
		S = new String[N];
		for(int i=0;i<N;i++) S[i] = rs();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}