CF2060C.Game of Mathletes

Alice and Bob are playing a game. There are $n$ ($n$ is even) integers written on a blackboard, represented by $x_1, x_2, \ldots, x_n$. There is also a given integer $k$ and an integer score that is initially $0$. The game lasts for $\frac{n}{2}$ turns, in which the following events happen sequentially:

• Alice selects an integer from the blackboard and erases it. Let's call Alice's chosen integer $a$.
• Bob selects an integer from the blackboard and erases it. Let's call Bob's chosen integer $b$.
• If $a+b=k$, add $1$ to score.

Alice is playing to minimize the score while Bob is playing to maximize the score. Assuming both players use optimal strategies, what is the score after the game ends?

爱丽丝和鲍勃正在玩一个游戏。黑板上写有 $n$（$n$ 为偶数）个整数，记为 $x_1, x_2, \ldots, x_n$。此外给定一个整数 $k$，以及一个初始值为 $0$ 的分数。游戏共进行 $\frac{n}{2}$ 轮，每轮依次发生以下事件：

• 爱丽丝从黑板上选择一个整数并将其擦除。记爱丽丝选择的整数为 $a$。
• 鲍勃从黑板上选择一个整数并将其擦除。记鲍勃选择的整数为 $b$。
• 若 $a+b=k$，则将分数加 $1$。

爱丽丝的目标是最小化最终分数，而鲍勃的目标是最大化最终分数。假设双方均采用最优策略，游戏结束时的分数是多少？

The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$ and $k$ ($2 \leq n \leq 2\cdot 10^5, 1 \leq k \leq 2\cdot n$, $n$ is even).

The second line of each test case contains $n$ integers $x_1,x_2,\ldots,x_n$ ($1 \leq x_i \leq n$) — the integers on the blackboard.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$.

第一行包含一个整数 $t$（$1 \leq t \leq 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$2 \leq n \leq 2\cdot 10^5$，$1 \leq k \leq 2\cdot n$，且 $n$ 为偶数）。

每个测试用例的第二行包含 $n$ 个整数 $x_1,x_2,\ldots,x_n$（$1 \leq x_i \leq n$）—— 黑板上的整数。

保证所有测试用例的 $n$ 之和不超过 $2\cdot 10^5$。

For each test case, output the score if both players play optimally.

对于每个测试用例，输出双方均采取最优策略时的得分。

In the first test case, one way the game may go is as follows:

• Alice selects $1$ and Bob selects $3$. The score increases as $1+3=4$. Now the two integers remaining on the blackboard are $2$ and $2$.
• Alice and Bob both select $2$. The score increases as $2+2=4$.
• The game ends as the blackboard now has no integers.

In the third test case, it is impossible for the sum of Alice and Bob's selected integers to be $1$, so we answer $0$.

Note that this is just an example of how the game may proceed for demonstration purposes. This may not be Alice or Bob's most optimal strategies.

在第一个测试用例中，游戏的一种可能进行方式如下：

• 爱丽丝选择 $1$，鲍勃选择 $3$。得分增加为 $1+3=4$。此时黑板上剩余的两个整数为 $2$ 和 $2$。
• 爱丽丝和鲍勃均选择 $2$。得分增加为 $2+2=4$。
• 游戏结束，因为黑板上已无整数。

在第三个测试用例中，爱丽丝与鲍勃所选整数之和不可能为 $1$，因此答案为 $0$。

注意：以上仅为演示游戏可能如何进行的一个示例。这未必是爱丽丝或鲍勃的最优策略。