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

• Alice starts with an integer $n$, and Bob starts with an integer $m$.
• Starting with Alice, the two players take turns performing an operation on the integer held by the opponent: let the integer currently held by the opponent be $h$, replace $h$ with $h - (h \bmod p)$, where $\bmod$ denotes the modulo operation and $p$ is a given constant.
• The first player to make the opponent's integer $0$ wins. If neither player has won after each has performed $10^{10^{9961}}$ operations, the game is considered a draw.

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

Input

This problem contains multiple test cases.

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

Each test case consists of three integers $n, m, p$.

Output

For each test case, output a single string on a new line:

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

Examples

Input 1

3
1 2 10
9 11 11
55 15 14

Output 1

Alice
Bob
Lasting Battle

Note 1

For the first test case, Alice will change the integer Bob holds from $2$ to $2 - (2 \bmod 10) = 0$ in her first turn, so Alice wins.

For the second test case, Alice will change the integer Bob holds from $11$ to $11 - (11 \bmod 11) = 11$ in her first turn, and Bob will change the integer Alice holds from $9$ to $9 - (9 \bmod 11) = 0$ in his first turn, so Bob wins.

For the third test case, it can be proven that the game will end in a draw.

Constraints

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