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.function.Consumer;
import java.util.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.io.*;
import java.lang.Math.*;
 public class KickStart2020{
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){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());}
        float nextFloat() {return Float.parseFloat(next());}
        String nextLine() {
            String str = "";
            try {str = br.readLine();}
            catch (IOException e) { e.printStackTrace();}
            return str; }}
	
	static String reverseOfString(String a) {
		StringBuilder ssd = new StringBuilder();
		for(int i = a.length() - 1; i >= 0; i--) {
			ssd.append(a.charAt(i));
		}
		return ssd.toString();
	}
	static String parsingString(String a) {
		StringBuilder ssd = new StringBuilder();
		for(int i = 0; i < a.length(); i++) {
			if(a.charAt(i) != '0') ssd.append(a.charAt(i));
		}
		return ssd.toString();
	}
	static boolean checker(String a) {
			boolean hachu = true;
			for(int i = 1; i < a.length(); i++) {
				if(a.charAt(i) < 65 || a.charAt(i) > 90) {
					hachu = false;
					break;
				}
			}
			return hachu;
		}
	static boolean checkers(String a) {
		boolean hachu = true;
		for(int i = 0; i < a.length(); i++) {
			if(a.charAt(i) < 65 || a.charAt(i) > 90) {
				hachu = false;
				break;
			}
		}
		return hachu;
	}
	static boolean isPalindrome(char a[]) {
		boolean hachu = true;
		for(int i = 0; i <= a.length / 2; i++) {
			if(a[i] != a[a.length - 1 - i]) {
				hachu = false;
				break;
			}
		}
		return hachu;
	}
	static boolean count(char a[], int n, int m) {
		int count1 = 0, count0 = 0;
		for(int i = 0; i < a.length; i++) {
			if(a[i] == '1') count1++;
			else count0++;
		}
		return (n == count0 && count1 == m) ? true: false;
	}
		public static void main(String[] args) throws Exception{
FastReader sc = new FastReader();
int t = sc.nextInt();
while(t-- > 0) {
	int n = sc.nextInt();
	long sum = 0;
	ArrayList<Integer> arr = new ArrayList<Integer>();
	for(int i = 0; i < n + 2; i++) {
		int a = sc.nextInt();
		sum += a;
		arr.add(a);}
	Collections.sort(arr);
	boolean hachu1 = false;
	int skip = 0;
	int max = 0;
	if(sum - arr.get(n + 1) - arr.get(n) == arr.get(n)) {
		max = n;
		skip = n + 1;
		hachu1 = true;
	}
	else {
		sum -= arr.get(n + 1);
		for(int i = 0; i < n + 1; i++) {
			if(sum - arr.get(i) == arr.get(n + 1)) {
				skip = i;
				max = n + 1;
				hachu1 = true;
				break;
			}
		}
	}
	if(hachu1) {
		for(int i = 0; i < n + 2; i++) {
			if(i != skip && i != max) System.out.print(arr.get(i) + " ");
		}
		System.out.println();
	}
	else System.out.println(-1);
 }
}
 }