1547_C. 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, ..., 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, ..., 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, ..., a_n] and Polycarp's — subsequence [b_1, b_2, ..., 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 ≤ t ≤ 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 ≤ k ≤ 100, 1 ≤ n, m ≤ 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, ..., a_n (0 ≤ a_i ≤ 300).

The third line contains m integers b_1, b_2, ..., b_m (0 ≤ b_j ≤ 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.

Example

Input


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


Output


2 0 0 5 
0 2 0 6 5 
-1
0 6 0 7 0 8 0 9
-1
```python
# -*- coding: utf-8 -*-
"""
Created on Sat Jul 10 23:15:34 2021

@author: Kevin Chang

Project: Codeforces Problem 1547C

"""

t = int(input())

for i in range(t):
    shit = input()
    k, n, m = list(map(int, input().split()))
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))
    res = []
    ress = 1

    for aa in a:
        if ress == -1:
            break
        elif aa == 0:
            k += 1
            res.append(aa)
        elif aa > k:
            while k < aa:
                if len(b) == 0:
                    ress = -1
                    break
                elif b[0] == 0:
                    k += 1
                    res.append(b.pop(0))
                elif b[0] > k:
                    ress = -1
                    break
                else:
                    res.append(b.pop(0))
            res.append(aa)
        else:
            res.append(aa)
            continue

    if ress == -1:
        print(ress)
    else:
        for bb in b:
            if ress == -1:
                break
            elif bb == 0:
                k += 1
                res.append(bb)
            elif bb > k:
                ress = -1
            else:
                res.append(bb)
            continue
        if ress == -1:
            print(ress)
        else:
            print(*res)

```