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.*;
public class A {
	public static void main(String args[]) {
		FastScanner in=new FastScanner();
		int t=in.nextInt();
		L: while(--t>=0) {
			int n=in.nextInt();
			int a[]=in.nextArray(n+2);
			ruffleSort(a);
			StringBuilder sb=new StringBuilder();
			long sum1=a[n];
			long sum2=0;
			for(int i=0;i<n;i++)
				sum2=sum2+a[i];
			if(sum1==sum2) {
				for(int i=0;i<n;i++)
					sb.append(a[i]+" ");
				System.out.println(sb);
				continue L;
			}
			sum1=a[n+1];
			sum2=0;
//			System.out.println(Arrays.toString(a));
			for(int i=0;i<n+1;i++)
				sum2=sum2+a[i];
			for(int i=0;i<n+1;i++) {
//				System.out.println(sum1+" "+sum2+" "+a[i]);
				if(sum2-a[i]==sum1) {
					for(int j=0;j<n+1;j++) {
						if(i!=j)
							sb.append(a[j]+" ");
					}
					System.out.println(sb);
					continue L;
				}
			}
			System.out.println(-1);
		}
	}

	///////////////////////////
	static void ruffleSort(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 FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");

		String next() {
			while (!st.hasMoreTokens())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		long nextLong() {
			return Long.parseLong(next());
		}
	}
}