CF1348B.Phoenix and Beauty

Phoenix loves beautiful arrays. An array is beautiful if all its subarrays of length $k$ have the same sum. A subarray of an array is any sequence of consecutive elements.

Phoenix currently has an array $a$ of length $n$. He wants to insert some number of integers, possibly zero, into his array such that it becomes beautiful. The inserted integers must be between $1$ and $n$ inclusive. Integers may be inserted anywhere (even before the first or after the last element), and he is not trying to minimize the number of inserted integers.

凤凰喜爱优美的数组。若一个数组的所有长度为 $k$ 的子数组的元素和均相等，则称该数组是优美的。数组的一个子数组是指其中任意一段连续的元素。

目前，凤凰拥有一个长度为 $n$ 的数组 $a$。他希望向该数组中插入若干个整数（可以不插入），使得其变为优美的数组。所插入的整数必须在 $1$ 到 $n$ 之间（含端点）。整数可插入到任意位置（甚至可在第一个元素之前或最后一个元素之后），且他并不试图最小化插入整数的个数。

The input consists of multiple test cases. The first line contains an integer $t$ ($1 \le t \le 50$) — the number of test cases.

The first line of each test case contains two integers $n$ and $k$ ($1 \le k \le n \le 100$).

The second line of each test case contains $n$ space-separated integers ($1 \le a_i \le n$) — the array that Phoenix currently has. This array may or may not be already beautiful.

输入包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 50$），表示测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$1 \le k \le n \le 100$）。

每个测试用例的第二行包含 $n$ 个以空格分隔的整数（$1 \le a_i \le n$），即凤凰当前拥有的数组。该数组可能已经美丽，也可能尚未美丽。

For each test case, if it is impossible to create a beautiful array, print -1. Otherwise, print two lines.

The first line should contain the length of the beautiful array $m$ ($n \le m \le 10^4$). You don't need to minimize $m$.

The second line should contain $m$ space-separated integers ($1 \le b_i \le n$) — a beautiful array that Phoenix can obtain after inserting some, possibly zero, integers into his array $a$. You may print integers that weren't originally in array $a$.

If there are multiple solutions, print any. It's guaranteed that if we can make array $a$ beautiful, we can always make it with resulting length no more than $10^4$.

对于每个测试用例，如果无法构造出优美的数组，则输出 -1。否则，输出两行。

第一行应包含优美数组的长度 $m$（满足 $n \le m \le 10^4$）。你无需使 $m$ 最小。

第二行应包含 $m$ 个以空格分隔的整数（满足 $1 \le b_i \le n$）——即凤凰在数组 $a$ 中插入若干（可能为零）个整数后所能得到的一个优美数组。你可以输出原本不在数组 $a$ 中的整数。

若存在多种解，输出任意一种即可。题目保证：若能将数组 $a$ 变为优美数组，则总存在一种方案使得最终数组长度不超过 $10^4$。

In the first test case, we can make array $a$ beautiful by inserting the integer $1$ at index $3$ (in between the two existing $2$s). Now, all subarrays of length $k=2$ have the same sum $3$. There exists many other possible solutions, for example:

• $2, 1, 2, 1, 2, 1$
• $1, 2, 1, 2, 1, 2$

In the second test case, the array is already beautiful: all subarrays of length $k=3$ have the same sum $5$.

In the third test case, it can be shown that we cannot insert numbers to make array $a$ beautiful.

In the fourth test case, the array $b$ shown is beautiful and all subarrays of length $k=4$ have the same sum $10$. There exist other solutions also.

在第一个测试用例中，我们可以通过在索引 $3$ 处（即两个已有的 $2$ 之间）插入整数 $1$，使数组 $a$ 变为优美的。此时，所有长度为 $k=2$ 的子数组的和均为 $3$。还存在许多其他可行解，例如：

• $2, 1, 2, 1, 2, 1$
• $1, 2, 1, 2, 1, 2$

在第二个测试用例中，该数组本身已是优美的：所有长度为 $k=3$ 的子数组的和均为 $5$。

在第三个测试用例中，可以证明：无法通过插入数字使数组 $a$ 变为优美。

在第四个测试用例中，所示的数组 $b$ 是优美的，且所有长度为 $k=4$ 的子数组的和均为 $10$。此外，也存在其他可行解。