Alice and Bob are playing a game.

There are $n$ monsters in the game, and they stand in a line. Alice and Bob take turns. Each turn, the player can choose one of two actions:

1. Destroy a consecutive monster sequence of size less than or equal to $K$.
2. Select $K$ consecutive monsters to destroy, and after destroying these $K$ monsters, the sequential monster sequence in which they were originally located must be divided into two non-empty sequences. The two remaining sequences will not be considered continuous.

Here is an example of operation 2: if $K = 2$ and there are four monsters $ABCD$ in the field, we can destroy monsters $BC$ because they are continuous, and after destroying them we can be left with monsters $AeeD$ ($e$ means the area is empty). But we cannot destroy the monsters $AB$ or $CD$, because the remaining two sequences must be non-empty (in fact, if we do this, only one continuous sequence remains). Similarly, we can’t destroy monsters $AC$ or $BD$ because monsters $A$ and $C$ are not continuous.

When a player cannot operate, he loses. Now, Alice will play the game first. She wants to know, can she win at this game?

Input

An integer $T$ indicates that there are $T$ groups of data. Next $T$ rows. Enter two integers $K$ and $n$ on each line. Guarantee $1 \le T \le 10000$, $2 \le K \le 10^7$, $0 \le n \le 10^9$.

Output

Output total $T$ lines. If Alice can win, output "Alice", otherwise output "Bob".

Examples

Input 1

2
2 2
2 3

Output 1

Alice
Bob