CF2147B.Multiple Construction

You are given an integer $n$. Your task is to construct an array of length $2 \cdot n$ such that:

• Each integer from $1$ to $n$ appears exactly twice in the array.
• For each integer $x$ ($1 \le x \le n$), the distance between the two occurrences of $x$ is a multiple of $x$. In other words, if $p_x$ and $q_x$ are the indices of the two occurrences of $x$, $| q_x - p_x |$ must be divisible by $x$.

It can be shown that a solution always exists.

给你一个整数 $n$。你的任务是构造一个长度为 $2 \cdot n$ 的数组，满足以下条件：

• 每个从 $1$ 到 $n$ 的整数在数组中恰好出现两次。
• 对于每个整数 $x$（$1 \le x \le n$），$x$ 的两次出现位置之间的距离是 $x$ 的倍数。换言之，若 $p_x$ 和 $q_x$ 分别表示 $x$ 的两次出现位置的下标，则 $| q_x - p_x |$ 必须能被 $x$ 整除。

可以证明，这样的解总是存在的。

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 of the next $t$ lines contains a single integer $n$ ($1 \le n \le 2 \cdot 10^{5}$).

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

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

接下来的 $t$ 行中，每行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^{5}$）。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^{5}$。

For each test case, print a line containing $2 \cdot n$ integers — the array that satisfies the given conditions.

If there are multiple valid answers, print any of them.

对于每个测试用例，输出一行包含 $2 \cdot n$ 个整数的数组——该数组需满足给定的条件。

若存在多个合法答案，输出其中任意一个即可。

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In the first test case:

• The number $1$ appears at positions $1$ and $3$: the distance is $2$, which is divisible by $1$.
• The number $2$ appears at positions $2$ and $4$: the distance is $2$, which is divisible by $2$.

In the second test case:

• The number $1$ appears at positions $1$ and $3$: the distance is $2$, which is divisible by $1$.
• The number $2$ appears at positions $4$ and $6$: the distance is $2$, which is divisible by $2$.
• The number $3$ appears at positions $2$ and $5$: the distance is $3$, which is divisible by $3$.

In the third test case, the two occurrences of $1$ are at positions $1$ and $2$, so the distance between them is $1$, which is a multiple of $1$.

可视化链接

在第一个测试用例中：

• 数字 $1$ 出现在位置 $1$ 和 $3$：距离为 $2$，可被 $1$ 整除。
• 数字 $2$ 出现在位置 $2$ 和 $4$：距离为 $2$，可被 $2$ 整除。

在第二个测试用例中：

• 数字 $1$ 出现在位置 $1$ 和 $3$：距离为 $2$，可被 $1$ 整除。
• 数字 $2$ 出现在位置 $4$ 和 $6$：距离为 $2$，可被 $2$ 整除。
• 数字 $3$ 出现在位置 $2$ 和 $5$：距离为 $3$，可被 $3$ 整除。

在第三个测试用例中，数字 $1$ 的两次出现位置分别为 $1$ 和 $2$，因此它们之间的距离为 $1$，是 $1$ 的倍数。