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;

#define all(v) v.begin(), v.end()

typedef long long ll;

void resp() {
    int n; cin >> n;
    int m = n + 2;
    vector<ll> b(m);
    for (auto &x: b) cin >> x;
    sort(all(b));
    vector<ll> S(m);
    S[0] = b[0];
    for (int i=1; i<m; i++) S[i] = S[i-1] + b[i];
    ll s = 0, x = 0;
    for (int i=0; i<m; i++) {
        if (i!=m-1 && b[m-1] == S[m-1] - b[m-1] - b[i]) {
            s = b[m-1];
            x = b[i];
        } else if (i!=m-2 && b[m-2] == S[m-1] - b[m-2] - b[i]) {
            s = b[m-2];
            x = b[i];
        }
    }

    if (s==0 || x==0) { cout << -1 << '\n'; return; }

    for (int i=0; i<m; i++) {
        if (b[i]==s && s>0) {
            s = 0; continue;
        }
        if (b[i]==x && x>0) {
            x = 0; continue;
        }
        cout << b[i] << " ";
    }
    cout << '\n';
}

int main() {

    ios_base::sync_with_stdio(false); cin.tie(0);

    int t; cin >> t;
    while (t--) {
        resp();        
    }
    return 0;
}