CF2181B.Battle of Arrays

Alice and Bob play a turn-based game. Initially, Alice has an array $a$ of $n$ positive integers, and Bob has an array $b$ of $m$ positive integers. The players take turns, with Alice moving first.

On a player's turn, they must choose one element $x$ from their own array and the maximal element $y$ from their opponent's array. Then they perform the following operation:

• If $y \leq x$: the element $y$ is destroyed (removed from the opponent's array).
• If $y \gt x$: the element $y$ is decreased by $x$ (the value of $y$ becomes $y - x$).

A player wins if, after their move, the opponent's array becomes empty.

Assuming both players play optimally, determine the winner.

爱丽丝和鲍勃进行一场回合制游戏。初始时，爱丽丝拥有一个包含 $n$ 个正整数的数组 $a$，鲍勃拥有一个包含 $m$ 个正整数的数组 $b$。双方轮流行动，爱丽丝先手。

在某位玩家的回合中，该玩家必须从自己的数组中选择一个元素 $x$，并从对手的数组中选择最大元素 $y$。然后执行以下操作：

• 若 $y \leq x$：元素 $y$ 被摧毁（即从对手的数组中移除）；
• 若 $y > x$：元素 $y$ 减少 $x$（即 $y$ 的值变为 $y - x$）。

若某位玩家在完成自己的操作后，使得对手的数组变为空，则该玩家获胜。

假设双方均以最优策略进行游戏，请判断最终的获胜者。

Each input contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$).

The first line of each test case contains two integers $n$ and $m$ ($1 \le n,m \le 10^5$) — the sizes of Alice's and Bob's arrays respectively.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$) — Alice's array.

The third line contains $m$ integers $b_1, b_2, \ldots, b_m$ ($1 \le b_i \le 10^9$) — Bob's array.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ and the sum of $m$ over all test cases does not exceed $10^5$.

每个输入包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^5$）。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le n,m \le 10^5$）—— 分别表示爱丽丝和鲍勃的数组长度。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$）—— 爱丽丝的数组。

第三行包含 $m$ 个整数 $b_1, b_2, \ldots, b_m$（$1 \le b_i \le 10^9$）—— 鲍勃的数组。

保证所有测试用例中 $n$ 的总和不超过 $10^5$，且所有测试用例中 $m$ 的总和不超过 $10^5$。

For each test case, print the name of the winner of the game if both players follow the optimal strategy: "Alice" or "Bob".

对于每个测试用例，若双方玩家均采用最优策略，则输出游戏获胜者的名字：“Alice”或“Bob”。

In the first test Alice moves and decreases Bob's element by $70$, so it becomes $20$. Then Bob moves and decreases Alice's element by $20$, so it becomes $50$. Finally, Alice moves, destroys Bob's element, and wins.

在第一组测试中，爱丽丝先行动，将鲍勃的元素减小 $70$，使其变为 $20$；接着鲍勃行动，将爱丽丝的元素减小 $20$，使其变为 $50$；最后爱丽丝行动，摧毁鲍勃的元素并获胜。