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 CPP):

Solution:
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=3e5+10;
const int M=1e3+10;
ll bi[N];
int pos,n;
ll sum=0;
int judge(int flag)
{
    if(flag==1)
    {
        ll temp=sum-bi[n+2];
        for(int i=n+1;i>=1;i--){
            if(bi[n+2]==temp-bi[i]){
                pos=i;
                return 1;
            }
        }
        return 0;
    }
    else if(flag==2){
        if(sum-bi[n+2]==2*bi[n+1]) return 1;
        else return 0;
    }
}
void solve()
{
    cin>>n;
    sum=0;
    for(int i=1;i<=n+2;i++){
        cin>>bi[i];
        sum+=bi[i];
    }
    sort(bi+1,bi+1+n+2);
    if(judge(1)){
        for(int i=1;i<=n+1;i++){
            if(i!=pos) cout<<bi[i]<<' ';
        }
        cout<<endl;
    }
    else if(judge(2))
    {
        for(int i=1;i<=n;i++){
            cout<<bi[i]<<' ';
        }
        cout<<endl;
    }
    else{
        cout<<-1<<endl;
    }
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int t;
    cin>>t;
    while(t--)
        solve();
    return 0;
}