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 $$$a_i \gt 0$$$, 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 $$$b_j \gt 0$$$, 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.

Input

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 $$$b_1, b_2, \dots, b_m$$$ ($$$0 \le b_j \le 300$$$).

Output

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.

Pair Programming

Examples