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:
import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.addAll(Arrays.asList(read.split(" ")));
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<String> nextStrArray(int size){
		ArrayList<String> ret = new ArrayList<>(size);
		for(int i = 0; i < size; i++){
			ret.add(next());
		}
		return ret;
	}
	static ArrayList<Integer> nextIntArray(int size){
		ArrayList<Integer> ret = new ArrayList<>(size);
		for(int i = 0; i < size; i++){
			ret.add(Integer.parseInt(next()));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(int size){
		ArrayList<Long> ret = new ArrayList<>(size);
		for(int i = 0; i < size; i++){
			ret.add(Long.parseLong(next()));
		}
		return ret;
	}
	@SuppressWarnings("unchecked")
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------

	static void solve(){//Here is the main function
		int t = nextInt();
		for(int i = 0; i < t; i++){
			int N = nextInt();
			ArrayList<Integer> list = nextIntArray(N + 2);
			long sum = 0;
			TreeMap<Integer, Integer> set = new TreeMap<>();
			for(int j = 0; j < N + 2; j++){
				int v = list.get(j);
				sum += v;
				if(set.containsKey(v)){
					set.put(v, set.get(v) + 1);
				}else{
					set.put(v, 1);
				}
			}
			boolean isOK = false;
			for(int j = 0; j < N + 2; j++){
				int v = list.get(j);
				long newSum = sum - v;
				if(set.get(v) == 1){
					set.remove(v);
				}else{
					set.put(v, set.get(v) - 1);
				}
				int max = set.lastKey();
				if((long)max * 2 == newSum){
					if(set.get(max) == 1){
						set.remove(max);
					}else{
						set.put(max, set.get(max) - 1);
					}
					isOK = true;
					break;
				}
				if(set.containsKey(v)){
					set.put(v, set.get(v) + 1);
				}else{
					set.put(v, 1);
				}
			}
			if(isOK){
				ArrayList<String> output = new ArrayList<>();
				Iterator<Integer> key = set.keySet().iterator();
				while(key.hasNext()){
					int c = key.next();
					for(int j = 0; j < set.get(c); j++){
						output.add(String.valueOf(c));
					}
					
				}
				myout(myconv(output, 8));
			}else{
				myout(-1);
			}
		}
	}
	//Method addition frame start



	//Method addition frame end
}