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:




//..............Learning.........//


import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.BigInteger;

public class D {

  // >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Starts <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //
static FastReader  sc  = new FastReader();
static PrintWriter out = new PrintWriter(System.out);

public static void main(String[] args) throws Exception {
//    try {
  int t = sc.nextInt();
  while (t-- > 0)
  D.go();
  out.flush();
//    } catch (Exception e) {
//      return;
//    }
}

static void go() {
int n=sc.nextInt();
int a[]=new int[n+2];
for(int i=0;i<n+2;i++) {
	a[i]=sc.nextInt();
}
int N=n+2;
sort(a);
int b[]=new int[2];
b[0]=a[n+1];b[1]=a[n];
long sum=0;
for(int i=0;i<N-1;i++) {
	sum+=a[i];
}
int pos=-1;
boolean f=false;
for(int i=0;i<N-1;i++) {
	if((sum-a[i])==a[n+1]) {
		pos=i;
		f=true;
		break;
	}
}
if(f==true) {
	for(int i=0;i<N-1;i++) {
		if(i!=pos) {
			out.print(a[i]+" ");
		}
		
}
out.println();
	return;
}
if(f==false) {
	long sum1=0;
	for(int i=0;i<N-2;i++) {
		sum1+=a[i];
	}
	if(sum1==a[n]) {
		for(int i=0;i<N-2;i++) {
			out.print(a[i]+" ");
		}
		out.println();
		return;
	}
	out.println(-1);
}



}

static long convert(String x) {
	long two=0;

	for(int i=0;i<x.length();i++) {
		two=two+pow(2,x.length()-1-i)*(x.charAt(i)-'0');
	}
	return two;
}
// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Code Ends <<<<<<<<<<<<<<<<<<<<<<<<<<<<< //


static void sort(long [] a) {
  ArrayList<Long> aa = new ArrayList<>();
  for (long  i : a) {
    aa.add(i);
  }Collections.sort(aa);  for (int i = 0; i < a.length; i++)
    a[i] = aa.get(i);	  }
static void sort(int [] a) {
  ArrayList<Integer> aa = new ArrayList<>();
  for (int  i : a) {
    aa.add(i);
  } Collections.sort(aa); for (int i = 0; i < a.length; i++)
    a[i] = aa.get(i); }
static long pow(long x, long y) {
  long res = 1l;
  while (y != 0) {
    if (y % 2 == 1) {
      res = x * res;
    }
    y /= 2;
    x = x * x;
  }
  return res;
}

//>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Fast IO <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< //

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());
  }

  String nextLine() {
    String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }
  }

}