A14441. Pair Programming

Monocarp and Polycarp are learning new programming techniques. Now they decided to try pair programming.

It's known that they have worked together on the same file for $n + m$ minutes. Every minute exactly one of them made one change to the file. Before they started, there were already $k$ lines written in the file.

Every minute exactly one of them does one of two actions: adds a new line to the end of the file or changes one of its lines.

Monocarp worked in total for $n$ minutes and performed the sequence of actions $[a_1, a_2, \dots, a_n]$ . If $a_i = 0$ , then he adds a new line to the end of the file. If $a_i > 0$ , then he changes the line with the number $a_i$ . Monocarp performed actions strictly in this order: $a_1$ , then $a_2$ , ..., $a_n$ .

Polycarp worked in total for $m$ minutes and performed the sequence of actions $[b_1, b_2, \dots, b_m]$ . If $b_j = 0$ , then he adds a new line to the end of the file. If $b_j > 0$ , then he changes the line with the number $b_j$ . Polycarp performed actions strictly in this order: $b_1$ , then $b_2$ , ..., $b_m$ .

Restore their common sequence of actions of length $n + m$ such that all actions would be correct — there should be no changes to lines that do not yet exist. Keep in mind that in the common sequence Monocarp's actions should form the subsequence $[a_1, a_2, \dots, a_n]$ and Polycarp's — subsequence $[b_1, b_2, \dots, b_m]$ . They can replace each other at the computer any number of times.

Let's look at an example. Suppose $k = 3$ . Monocarp first changed the line with the number $2$ and then added a new line (thus, $n = 2, \: a = [2, 0]$ ). Polycarp first added a new line and then changed the line with the number $5$ (thus, $m = 2, \: b = [0, 5]$ ).

Since the initial length of the file was $3$ , in order for Polycarp to change line number $5$ two new lines must be added beforehand. Examples of correct sequences of changes, in this case, would be $[0, 2, 0, 5]$ and $[2, 0, 0, 5]$ . Changes $[0, 0, 5, 2]$ (wrong order of actions) and $[0, 5, 2, 0]$ (line $5$ cannot be edited yet) are not correct.

The first line contains an integer $t$ ( $1 \le t \le 1000$ ). Then $t$ test cases follow. Before each test case, there is an empty line.

Each test case contains three lines. The first line contains three integers $k$ , $n$ , $m$ ( $0 \le k \le 100$ , $1 \le n, m \le 100$ ) — the initial number of lines in file and lengths of Monocarp's and Polycarp's sequences of changes respectively.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i \le 300$ ).

The third line contains $m$ integers $b_1, b_2, \dots, b_m$ ( $0 \le b_j \le 300$ ).

For each test case print any correct common sequence of Monocarp's and Polycarp's actions of length $n + m$ or -1 if such sequence doesn't exist.