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;
typedef long double ld;
#define int long long
//typedef pair<int, int> pii;
#define F first
#define S second
#define PB push_back
#define MP make_pair
const ll mod = 1e9 + 7, N = 2e6 + 7, M = 2e6 + 7, INF = INT_MAX / 10;
ll powe(ll x, ll y)
{
    x = x % mod, y = y % (mod - 1);
    ll ans = 1;
    while (y > 0)
    {
        if (y & 1)
        {
            ans = (1ll * x * ans) % mod;
        }
        y >>= 1;
        x = (1ll * x * x) % mod;
    }
    return ans;
}

void anmol()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
}



void solve()
{
 
int n;
cin>>n;

int a[n+2];
set<int> st;
map<int,int> mp;
for(int i =0; i<n+2; i++){
    cin>>a[i];
    //st.insert(a[i]);
    mp[a[i]]++;
}

sort(a,a+n+2);

int s =0;
for(int i =0; i<n; i++){
    s+=a[i];
}

if(s==a[n]){

    for(int i =0; i<n; i++){
        cout<<a[i]<<" ";

    }

    cout<<endl;
    return;
}


else {

    s+=a[n];
    for(int i =0; i<n+1; i++){
     if(s-a[i]==a[n+1]){
      for(int j =0; j<n+1; j++){
          if(i!=j){
              cout<<a[j]<<" ";
          }
      }

      cout<<endl;
      return;
     }
    }
}

cout<<-1<<endl;


}

int32_t main()
{
    int z =1;
    anmol();
    int t = 1;
    cin >> t;
    while (t--)
    {   //cout<<"Case #"<<z<<": ";
        //z++;
        solve();
    }
    return 0;
}