AT_arc229_d.Nim_k ?

There are $K+1$ piles of stones. The $i$-th pile has $A_i$ stones.
Alice and Bob play a game. In this game, they alternately take turns with Alice moving first. On each turn, the following operation is performed exactly $K$ times.

• Choose a pile with one or more stones, and remove one or more stones from it. Here, the same pile may be chosen multiple times within the same turn.

The player who is unable to perform the operation $K$ times on their own turn loses the game. Which player wins when both players play optimally?

You are given $T$ test cases; solve each of them.

共有 $K+1$ 堆石子。第 $i$ 堆有 $A_i$ 颗石子。
Alice 和 Bob 进行一场游戏，两人轮流行动，Alice 先手。在每一轮中，必须恰好执行 $K$ 次以下操作：

• 选择一堆至少含有一颗石子的石子堆，并从中移除一颗或更多石子。注意：在同一轮中，可以多次选择同一堆石子。

若某位玩家在其回合内无法完成 $K$ 次操作，则该玩家输掉游戏。当双方均采取最优策略时，谁将获胜？

你将得到 $T$ 组测试数据，请对每一组求解。

The input is given from Standard Input in the following format:

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

Each test case $\mathrm{case}_t$ is given in the following format:

$K$
$A_1$ $A_2$ $\dots$ $A_{K+1}$

输入从标准输入中按以下格式给出：

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

每个测试用例 $\mathrm{case}_t$ 按以下格式给出：

$K$
$A_1$ $A_2$ $\dots$ $A_{K+1}$

Output $T$ lines. The $i$-th line should contain Alice if Alice wins when both players play optimally for the $i$-th test case, and Bob if Bob wins.

输出 $T$ 行。第 $i$ 行应包含 Alice（若在第 $i$ 个测试用例中双方均采取最优策略时 Alice 获胜），或 Bob（若 Bob 获胜）。

Sample 1 Explanation:
Consider the first test case.
For example, suppose Alice performs the following operations on her first turn.

• Choose the second pile, and remove two stones from it. The number of stones in the second pile becomes $0$.
• Choose the third pile, and remove three stones from it. The number of stones in the third pile becomes $0$.

After her turn ends, only one stone remains. Therefore, Bob cannot perform the operation twice, so Alice wins.

In the second test case, every time Alice removes stones from one pile, Bob can remove the same number of stones from the other pile. By acting in this way, Bob can win.

Constraints

• $1 \leq T \leq 2 \times 10^5$
• $1 \leq K \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^9$
• The sum of $K$ over all test cases is at most $2 \times 10^5$.
• All input values are integers.

样例 1 解释：
考虑第一个测试用例。
例如，假设爱丽丝在她的第一回合执行以下操作：

• 选择第二堆石子，并从中移除两颗石子。第二堆石子的数量变为 $0$。
• 选择第三堆石子，并从中移除三颗石子。第三堆石子的数量变为 $0$。

在她这一回合结束后，仅剩一颗石子。因此，鲍勃无法执行两次操作，爱丽丝获胜。

在第二个测试用例中，每当爱丽丝从某一堆石子中移除若干颗石子时，鲍勃总能从另一堆石子中移除相同数量的石子。通过采取这种方式，鲍勃可以获胜。

约束条件

• $1 \leq T \leq 2 \times 10^5$
• $1 \leq K \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^9$
• 所有测试用例中 $K$ 的总和不超过 $2 \times 10^5$。
• 所有输入值均为整数。