Problem: You are given a number n and an array b_1, b_2, …, b_{n+2}, obtained according to the following algorithm: 

  * some array a_1, a_2, …, a_n was guessed; 
  * array a was written to array b, i.e. b_i = a_i (1 ≤ i ≤ n); 
  * The (n+1)-th element of the array b is the sum of the numbers in the array a, i.e. b_{n+1} = a_1+a_2+…+a_n; 
  * The (n+2)-th element of the array b was written some number x (1 ≤ x ≤ 10^9), i.e. b_{n+2} = x; The 
  * array b was shuffled. 



For example, the array b=[2, 3, 7, 12 ,2] it could be obtained in the following ways: 

  * a=[2, 2, 3] and x=12; 
  * a=[3, 2, 7] and x=2. 



For the given array b, find any array a that could have been guessed initially.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second row of each test case contains n+2 integers b_1, b_2, …, b_{n+2} (1 ≤ b_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output: 

  * "-1", if the array b could not be obtained from any array a; 
  * n integers a_1, a_2, …, a_n, otherwise. 



If there are several arrays of a, you can output any.

Example

Input


4
3
2 3 7 12 2
4
9 1 7 1 6 5
5
18 2 2 3 2 9 2
3
2 6 9 2 1


Output


2 3 7 
-1
2 2 2 3 9 
1 2 6 

Solution (in JAVA):

Solution:
// Main Code at the Bottom
import java.util.*;
import java.io.*; 
public class Main{
	//Fast IO class
    static class FastReader {
        BufferedReader br; 
        StringTokenizer st; 
        public FastReader() {
        	boolean env=System.getProperty("ONLINE_JUDGE") != null;
        	//env=true;
        	if(!env) {
        		try {
					br=new BufferedReader(new FileReader("src\\input.txt"));
				} catch (FileNotFoundException e) {
					e.printStackTrace();
				}
        	}
        	else br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) {
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
        int nextInt() {
            return Integer.parseInt(next()); 
        } 
        long nextLong() {
            return Long.parseLong(next()); 
        } 
        double nextDouble() {
            return Double.parseDouble(next()); 
        } 
        String nextLine() {
            String str = ""; 
            try {
                str = br.readLine(); 
            } 
            catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }     
    static long MOD=(long)1e9+7;
    //debug
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
    static FastReader sc=new FastReader();
    static PrintWriter out=new PrintWriter(System.out);  
    //Global variables and functions
    //Main function(The main code starts from here)
    public static void main (String[] args) throws java.lang.Exception {
    	int test=1;
    	test=sc.nextInt();
    	while(test-->0) {
    		int n=sc.nextInt()+2;
    		Long a[]=new Long[n];
    		long sum = 0;
    		for(int i=0;i<n;i++) sum+=a[i]=sc.nextLong();
    		Arrays.parallelSort(a,Collections.reverseOrder());
    		long s=sum-a[0];
    		boolean flag=false;
    		int idx=-1;
    		for(int i=1;i<n;i++) {
    			if(s-a[i]==a[0]) {
    				flag=true;
    				idx=i;
    				break;
    			}
    		}
    		if(flag) {
    			for(int i=1;i<n;i++) {
    				if(i!=idx) out.print(a[i]+" ");
    			}
    		}
    		else {
    			if(s-a[1]==a[1]) {
    				for(int i=2;i<n;i++) out.print(a[i]+" ");
    			}
    			else out.print(-1);
    		}
    		out.println();
    	}
        out.flush();
        out.close();
    }
}