You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
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.

## Input Format
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 $$$10^5$$$.

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

## Examples
```input
5
1 2
1
3 1
0 1 3
2 2
0 2
5 5
1 2 3 4 5
10 100
5 3 0 4 2 1 6 9 10 8
```
```output
1
2 0 1
2 1
2 3 4 5 0
7 5 3 0 4 2 1 6 9 10
```

## Note
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: $$$[{\mkern3mu\underline{\mkern-3mu {\bf 1}\mkern-3mu}\mkern3mu}, 0] \rightarrow [2, {\mkern3mu\underline{\mkern-3mu {\bf 0}\mkern-3mu}\mkern3mu}] \rightarrow [2, 1]$$$.

Now solve the problem and return the code.