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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class A {

    private static void addEles(long[] a, List<Long> b, int i, int si) {
        int it = 0, n = a.length;
        for (int j = 0; j < n + 2; j++) {
            if (j != si && j != i) a[it++] = b.get(j);
        }
    }
    public static void main(String[] args) {
        FastScanner fs=new FastScanner();
        PrintWriter pr = new PrintWriter(System.out);
        int T=fs.nextInt();
        for (int tt=1; tt<=T; tt++) {
            int n = fs.nextInt();
            List<Long> b = new ArrayList<>();
            for(int i = 0; i < n + 2; i++) b.add(fs.nextLong());
            Collections.sort(b);
            long s = 0; for(long i: b) s += i;

            long[] a = new long[n]; boolean f = false;
            for(int i = 0; i < n + 2; i++) {
                if((s - b.get(n + 1) - b.get(i)) == b.get(n + 1)) {
                    int si = n + 1;
                    if (si != i) {
                        addEles(a, b, i, si);
                        f = true;
                        break;
                    }
                }
                if((s - b.get(n) - b.get(i)) == b.get(n)) {
                    int si = n;
                    if (si != i) {
                        addEles(a, b, i, si);
                        f = true;
                        break;
                    }
                }
            }
            if(f) {
                for(int i = 0; i < n;i++) {
                    pr.print(a[i]);
                    if(i < n -1) pr.print(" ");
                }
                pr.println();
            } else pr.println(-1);
        }
        pr.flush();pr.close();
    }

    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[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long[] readLongArray(int n) {
            long[] a=new long[n];
            for (int i=0; i<n; i++) a[i]=nextLong();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}