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 <vector>
#include <cmath>
#include <string>
#include <set>
#include <map>
#include <deque>
#include <algorithm>
#include <queue>
#include <ctime>
#include <unordered_set>
#include <unordered_map>
#include <cassert>
#include <random>
#include <chrono>
#include <list>
#include <stack>
#include <bitset>
using namespace std;

//#define int ll

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair <int , int> pii;
typedef pair <ll , ll> pll;
typedef pair <ld , ld> pld;


#define ff first
#define ss second
#define mp make_pair
#define pf push_front
#define pb push_back
#define IO ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define print(x) { for (auto xxxxxxxxx : (x)) cout << xxxxxxxxx << ' '; cout << '\n'; }
#define printp(x) { for (auto xxxxxxxxx : (x)) cout << "{" << xxxxxxxxx.ff << ", " << xxxxxxxxx.ss << "} "; cout << '\n'; }
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()

const ll mod=1e9+7, mod2=1e9+9;
const ll inf=1e9;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//mt19937 rng(1337);
ll random(ll l, ll r){ return uniform_int_distribution<ll>(l, r)(rng);}

void solve(){
    int n;
    cin >> n;
    vector<ll> a(n+2);
    map<ll, int> use;
    ll sum = 0;
    for(auto &i: a){
        cin >> i;
        use[i]++;
        sum += i;
    }
    for(int i=0;i<n+2;i++){
        ll ts = sum - a[i];
        use[a[i]]--;
        if(ts%2 == 0 && use[ts/2] != 0){
            bool was = false;
            for(int j=0;j<n+2;j++){
                if(j == i) continue;
                if(a[j] == ts/2 && !was) was = true;
                else cout << a[j] << ' ';
            }
            cout << '\n';
            return;
        }
        use[a[i]]++;
    }
    cout << "-1\n";
}
/*

*/
signed main(){
    IO
    //freopen(".in" , "r" , stdin); freopen(".out" , "w" , stdout);
    int test = 1;
    cin >> test;
    while (test--){
        solve();
    }
}