Cossack Vus and the Game

Kozak Vus has devised another challenge for the olympiad participants!

You are given a collection of $n$ strings $s_1,s_2,\dots ,s_n$ and a number $k$.

A set of strings is considered good if:

1. Each string is composed solely of the characters $0$ and $1$;

2. The length of each string does not exceed $k$;

3. No string is a prefix of any other string in the set.

The provided set is already good.

Alice and Bob are engaged in the following game. They will alternate turns. During a turn, a player can add one string to the set as long as the set remains good. The player who cannot make a move loses the game.

Alice takes the first turn. Determine who will win if both players play optimally.

Input

The first line contains two integers $n$ ($0\le n\le 10^5,1\le k\le 10^{18}$) — the number of strings in the set and the maximum permissible length of a string in a good set.

The next $n$ lines each contain one of the strings. The $i$-th line contains the string $s_i$ ($1\le |s_i|\le 10^6$).

It is guaranteed that ${\sum }_{i=1}^n|s_i|\le 10^6$.

It is also guaranteed that the initial set is good.

Output

Output «Alice», if Alice will win, or «Bob», if Bob will win.

Examples

Scoring

1. ($2$ points): $n=0$;

2. ($6$ points): $k=2$;

3. ($8$ points): $k=3$;

4. ($12$ points): $k\le 10$;

5. ($17$ points): $k\le 20$;

6. ($20$ points): $k\le 10^4$;

7. ($35$ points): no additional constraints