Pair Programming

题意翻译

初始有 $k$ 行，给定两个操作序列 $a$ 和 $b$ ，你需要将它们合并为一个操作序列，需保证它在原数列中的相对位置不变。将操作序列依次操作，如果操作为 $0$ 则将 $k$ 加一，若不为 $0$ 且大于 $k$ ，则该序列不合法。问是否存在合法序列，如果有请给出一个。若没有，则输出 `-1` 。

题目描述

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.

输入输出格式

输入格式

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 $ ).

输出格式

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.

输入输出样例

输入样例 #1

5

3 2 2
2 0
0 5

4 3 2
2 0 5
0 6

0 2 2
1 0
2 3

5 4 4
6 0 8 0
0 7 0 9

5 4 1
8 7 8 0
0

输出样例 #1

2 0 0 5 
0 2 0 6 5 
-1
0 6 0 7 0 8 0 9
-1