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 <bits/stdc++.h>

using namespace std;


typedef long long ll;

//int xrow[8]={0,  0, -1, 1, -1, 1, -1,  1};
//int xcol[8]={1, -1,  0, 0,  1, 1, -1, -1};

//ll gcd(ll a, ll b){return b ? gcd(b, a%b) : a;}
//ll lcm(ll a, ll b){return a * b / gcd(a, b);}
const int N = 200100, MOD = 1e9 + 7, M = 3000;
int t, n, a[N];
int main(){
    //freopen("input.in","r",stdin);   //EOF
    //freopen("output.txt","w",stdout);
    cin >> t;
    while(t--){
        cin >> n;
        n += 2;
        ll sum = 0;
        for(int i = 0; i < n; ++i){
            cin >> a[i];
            sum += a[i];
        }
        sort(a, a + n);
        int fi = -1, se = -1;
        ll x;
        for(int i = 0; i < n - 1; ++i){
            if(i == n - 2){
                x = sum - a[n - 1] - a[n - 2];
                if(x == a[n - 1] || x == a[n - 2]){
                    fi = n - 1;
                    se = n - 2;
                    break;
                }
            }
            else{
                x = sum - a[n - 1] - a[i];
                if(x == a[n - 1]){
                    fi = i;
                    se = n - 1;
                }
                x = sum - a[n - 2] - a[i];
                if(x == a[n - 2]){
                    fi = i;
                    se = n - 2;
                }
            }
        }
        if(fi == -1){
            cout << fi << endl;
        }
        else{

        for(int i = 0; i < n; ++i){
            if(i == fi || i == se)
                continue;
            cout << a[i] << " ";
        }
        puts("");

        }

    }
    return 0;

}