Prefix-free Game

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.

Examples

Input

2 2 00 01

Output

Alice

Input

2 2 00 11

Output

Bob

Input

3 3 0 10 110

Output

Alice

Input

2 1 0 1

Output

Bob

Input

1 2 11

Output

Alice

Input

2 3 101 11

Output

Bob

inputFormat

Input

Input is given from Standard Input in the following format:

N L s_1 s_2 : s_N

outputFormat

Output

If Alice will win, print Alice; if Bob will win, print Bob.

Examples

Input

2 2 00 01

Output

Alice

Input

2 2 00 11

Output

Bob

Input

3 3 0 10 110

Output

Alice

Input

2 1 0 1

Output

Bob

Input

1 2 11

Output

Alice

Input

2 3 101 11

Output

Bob

样例

3 3
0
10
110

Alice