Problem Description

Alice and Bob are playing a game with the following rules:

• Alice initially has an integer $n$, and Bob initially has an integer $m$.
• Starting from Alice, the two players take turns operating on the integer owned by the other player. Let the integer currently owned by the other player be $h$. Change $h$ by subtracting $h \bmod p$ from it, where $\bmod$ denotes the modulo operation, and $p$ is a given constant.
• The first player who makes the other player's integer become $0$ wins. If no one wins after each of them has made $10^{10^{9961}}$ moves, the game is considered a draw.

You need to determine who will win, or report that the game will end in a draw.

Input Format

This problem has multiple test cases.

The first line contains an integer $T$, representing the number of test cases.

Then follow the test cases. For each test case, three integers $n, m, p$ are given.

Output Format

For each test case, output one string per line as the answer:

• If Alice will win, output Alice.
• If Bob will win, output Bob.
• If the game will be a draw, output Lasting Battle.

3
1 2 10
9 11 11
55 15 14

Alice
Bob
Lasting Battle

Hint

"Sample Explanation #1"

For the $1$st test case, in her first move, Alice changes Bob's integer from $2$ to $2-(2\bmod 10)$, which is $0$, so Alice will win.

For the $2$nd test case, in her first move, Alice changes Bob's integer from $11$ to $11-(11\bmod 11)$, which is $11$. In Bob's first move, he changes Alice's integer from $9$ to $9-(9 \bmod 11)$, which is $0$, so Bob will win.

For the $3$rd test case, it can be proven that the game will be a draw.

"Constraints"

For all testdata, $1 \leq T \leq 5000$, $1 \leq n, m, p \leq 2\times 10^9$.

Only if you pass all test points of this problem can you get the score for this problem.

Translated by ChatGPT 5