CF1863C.MEX Repetition

You are given an array $a_1,a_2,\ldots, a_n$ of pairwise distinct integers from $0$ to $n$. Consider the following operation:

• consecutively for each $i$ from $1$ to $n$ in this order, replace $a_i$ with $\operatorname{MEX}(a_1, a_2, \ldots, a_n)$.

Here $\operatorname{MEX}$ of a collection of integers $c_1, c_2, \ldots, c_m$ is defined as the smallest non-negative integer $x$ which does not occur in the collection $c$. For example, $\operatorname{MEX}(0, 2, 2, 1, 4) = 3$ and $\operatorname{MEX}(1, 2) = 0$.

Print the array after applying $k$ such operations.

给你一个由 $0$ 到 $n$ 之间的两两互异整数构成的数组 $a_1,a_2,\ldots, a_n$。考虑如下操作：

• 按照 $i$ 从 $1$ 到 $n$ 的顺序，依次将每个 $a_i$ 替换为 $\operatorname{MEX}(a_1, a_2, \ldots, a_n)$。

其中，整数集合 $c_1, c_2, \ldots, c_m$ 的 $\operatorname{MEX}$ 定义为未在该集合中出现的最小非负整数 $x$。例如，$\operatorname{MEX}(0, 2, 2, 1, 4) = 3$，而 $\operatorname{MEX}(1, 2) = 0$。

请输出对该数组执行 $k$ 次上述操作后的结果。

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

The first line of each test case contains two integers $n$ and $k$ ($1\le n\le 10^5$, $1\le k\le 10^9$).

The second line contains $n$ pairwise distinct integers $a_1,a_2,\ldots, a_n$ ($0\le a_i\le n$) representing the elements of the array before applying the operations.

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

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^5$）。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$1\le n\le 10^5$，$1\le k\le 10^9$）。

第二行包含 $n$ 个两两不同的整数 $a_1,a_2,\ldots, a_n$（$0\le a_i\le n$），表示执行操作前数组的元素。

保证所有测试用例的 $n$ 之和不超过 $10^5$。

For each test case, print all $n$ elements of the array after applying $k$ operations.

对于每个测试用例，输出执行 $k$ 次操作后数组的全部 $n$ 个元素。

In the first test case, here is the entire process:

1. On the first operation, the array changes from $[1]$ to $[0]$, since $\operatorname{MEX}(1) = 0$.
2. On the second operation, the array changes from $[0]$ to $[1]$, since $\operatorname{MEX}(0) = 1$.

Thus, the array becomes $[1]$ after two operations.

In the second test case, the array changes as follows during one operation: $[{\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}, 1, 3] \rightarrow [2, {\mkern3mu\underline{\mkern-3mu {\bf 1}\mkern-3mu}\mkern3mu}, 3] \rightarrow [2, 0, {\mkern3mu\underline{\mkern-3mu {\bf 3}\mkern-3mu}\mkern3mu}] \rightarrow [2, 0, 1]$.

In the third test case, the array changes as follows during one operation: $[{\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}, 2] \rightarrow [1, {\mkern3mu\underline{\mkern-3mu {\bf 2}\mkern-3mu}\mkern3mu}] \rightarrow [1, 0]$. And during the second operation: $[{\mkern3mu\underline{\mkern-3mu {\bf 1}\mkern-3mu}\mkern3mu}, 0] \rightarrow [2, {\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}] \rightarrow [2, 1]$.

在第一个测试用例中，整个过程如下：

1. 在第一次操作中，数组从 $[1]$ 变为 $[0]$，因为 $\operatorname{MEX}(1) = 0$。
2. 在第二次操作中，数组从 $[0]$ 变为 $[1]$，因为 $\operatorname{MEX}(0) = 1$。

因此，经过两次操作后，数组变为 $[1]$。

在第二个测试用例中，数组在一次操作中的变化过程如下：$[{\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}, 1, 3] \rightarrow [2, {\mkern3mu\underline{\mkern-3mu {\bf 1}\mkern-3mu}\mkern3mu}, 3] \rightarrow [2, 0, {\mkern3mu\underline{\mkern-3mu {\bf 3}\mkern-3mu}\mkern3mu}] \rightarrow [2, 0, 1]$。

在第三个测试用例中，数组在一次操作中的变化过程如下：$[{\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}, 2] \rightarrow [1, {\mkern3mu\underline{\mkern-3mu {\bf 2}\mkern-3mu}\mkern3mu}] \rightarrow [1, 0]$；在第二次操作中：$[{\mkern3mu\underline{\mkern-3mu {\bf 1}\mkern-3mu}\mkern3mu}, 0] \rightarrow [2, {\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}] \rightarrow [2, 1]$。