CF2196A.Game with a Fraction

Alice and Bob have two integers $p$ and $q$, and they are playing a game with these numbers. The players take turns, with Alice going first. On their turn, a player can do one of two actions:

• decrease $p$ by one (this action is possible if $p \gt 0$);
• decrease $q$ by one (this action is possible if $q \gt 1$).

The game ends when $p = 0$ and $q = 1$.

Bob wins if at any point during the game the fraction $\frac{p}{q}$ is equal to in value the fraction $\frac{2}{3}$. Otherwise, Alice wins.

Given the initial values of $p$ and $q$, determine the winner of the game if both players play optimally.

Alice 和 Bob 有两个整数 $p$ 和 $q$，他们正用这两个数进行一场游戏。双方轮流行动，Alice 先手。在每一轮中，当前玩家可以执行以下两种操作之一：

• 将 $p$ 减少 1（该操作仅在 $p > 0$ 时可行）；
• 将 $q$ 减少 1（该操作仅在 $q > 1$ 时可行）。

当 $p = 0$ 且 $q = 1$ 时，游戏结束。

若在游戏过程中的任意时刻，分数 $\frac{p}{q}$ 的值恰好等于 $\frac{2}{3}$，则 Bob 获胜；否则 Alice 获胜。

给定初始的 $p$ 和 $q$，假设双方均以最优策略进行游戏，请判断游戏的获胜者。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

Each input case consists of a single line containing two integers $p$ and $q$ ($1 \le p, q \le 10^{18}$).

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^4$）。随后是各测试用例的描述。

每个输入用例由一行组成，包含两个整数 $p$ 和 $q$（$1 \le p, q \le 10^{18}$）。

For each input case, output:

• "Alice" if Alice wins;
• "Bob" if Bob wins.

对于每个输入样例，输出：

• 若 Alice 获胜，输出 “Alice”；
• 若 Bob 获胜，输出 “Bob”。

In the first input case, the fraction is already equal to $\frac{2}{3}$ by value, so Bob wins.

In the second input case, one possible sequence of the game is as follows:

• initially $p = 10, q = 14$;
• after Alice's turn $p = 9, q = 14$;
• after Bob's turn $p = 9, q = 13$;
• after Alice's turn $p = 9, q = 12$;
• after Bob's turn $p = 8, q = 12$.

Bob wins, as $\frac{8}{12}$ is equal to $\frac{2}{3}$. It can be shown that in this example, with optimal play from both players, Bob always wins.

For the third input case, Alice's optimal strategy will be to decrease $q$ as long as possible. In this case, the game will end in favor of Alice regardless of Bob's actions.

在第一个输入样例中，该分数的值已等于 $\frac{2}{3}$，因此鲍勃获胜。

在第二个输入样例中，游戏的一种可能进行序列如下：

• 初始时 $p = 10, q = 14$；
• 爱丽丝操作后 $p = 9, q = 14$；
• 鲍勃操作后 $p = 9, q = 13$；
• 爱丽丝操作后 $p = 9, q = 12$；
• 鲍勃操作后 $p = 8, q = 12$。

由于 $\frac{8}{12}$ 等于 $\frac{2}{3}$，鲍勃获胜。可以证明，在本例中，若双方均采取最优策略，则鲍勃总能获胜。

在第三个输入样例中，爱丽丝的最优策略是尽可能多地减少 $q$。此时，无论鲍勃如何行动，游戏最终都将对爱丽丝有利。