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.

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.

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.
• $|s_1| + |s_2| + ... + |s_N| \leq 10^5$

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

见题面 Input 部分

见题面 Output 部分