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
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

public class java1 {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }
    static class TaskB {

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int t=in.nextInt();
            outer: while(t-- >0)
            {
            	int k=in.nextInt();
            	int n=in.nextInt();
            	int m=in.nextInt();
            	int na[]=in.inputarInt(n); int A=0;
            	int ma[]=in.inputarInt(m); int B=0;
            	int ans[]=new int[n+m];
            	
            	for(int x=1;x<=n+m;x++)
            	{
            		if(A<=n-1 && na[A]==0)
            		{
            			ans[x-1]=0;
            			A++;
            			k++;
            		}
            		else if(B<=m-1 &&ma[B]==0)
            		{
            			ans[x-1]=0;
            			k++;
            			B++;
            		}
            		else if(A<=n-1 && B<= m-1)
            		{
            			if(na[A] <=ma[B])
            			{
            				if(na[A] <=k)
            				{
            					ans[x-1]=na[A];
            					A++;
            				}
            				else
            				{
            					out.println("-1"); continue outer;
            				}
            			}
            			else
            			{
            				if(ma[B] <=k)
            				{
            					ans[x-1]=ma[B];
            					B++;
            				}
            				else
            				{
            					out.println("-1"); continue outer;
            				}
            			}
            		}
            		else if(A<=n-1)
            		{
            			if(na[A] <=k)
        				{
        					ans[x-1]=na[A];
        					A++;
        				}
        				else
        				{
        					out.println("-1"); continue outer;
        				}
            		}
            		else
            		{
            			if(ma[B] <=k)
        				{
        					ans[x-1]=ma[B];
        					B++;
        				}
        				else
        				{
        					out.println("-1"); continue outer;
        				}
            		}
            	}
            	for(int x=0;x<n+m;x++)
            	{
            		out.print(ans[x]+" ");
            	}
out.println();            	
            	
            	
            	
            			
            }
        }
        static void sort(int[] a) {
    		ArrayList<Integer> l=new ArrayList<>();
    		for (int i:a) l.add(i);
    		Collections.sort(l);
    		for (int i=0; i<a.length; i++) a[i]=l.get(i);
    	}
        
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int[] inputarInt(int n)
        {
        	int ar[]=new int[n];
        	for(int x=0;x<n;x++)
        	{
        		ar[x]=nextInt();
        	}
        	return ar;
        }
        public long[] inputarLong(int n)
        {
        	long ar[]=new long[n];
        	for(int x=0;x<n;x++)
        	{
        		ar[x]=nextLong();
        	}
        	return ar;
        }
    }
}