Problem Statement

There are positive integers $N$ and $M$, where $N \lt M$. Alice and Bob will play a game. Each player has $N$ cards with $1, 2, \dots, N$ written on them, one for each number. Starting with Alice, the two players take turns repeatedly performing this action: choose one card from their hand and play it onto the table. Immediately after a card is played onto the table, if the sum of the numbers on the cards that have been played so far is divisible by $M$, the player who just played the card loses, and the other player wins. If both players play all their cards without satisfying the above condition, Alice wins. Who will win, Alice or Bob, when both play optimally?

You are given $T$ test cases. Solve each of them.

Constraints

• $1 \leq T \leq 10^5$
• $1 \leq N \lt M \leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format. Here, $\mathrm{case}_i$ denotes the $i$-th test case.

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each test case is given in the following format:

N M

Output

Print $T$ lines. The $i$-th line should contain the answer for the $i$-th test case. For each test case, if Alice wins when both play optimally, print Alice; if Bob wins, print Bob.