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:
/*
Code by: tush_chen
*/

#include <bits/stdc++.h>

using namespace std;

string to_string(string s) {
    return '"' + s + '"';
}

string to_string(const char* s) {
    return to_string((string) s);
}

string to_string(bool b) {
    return (b ? "true" : "false");
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}

#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

#define pb push_back
#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll) (x).size())
#define endl '\n'

typedef long long ll;
typedef vector <ll> vi;
typedef pair <ll, ll> pi;

void solve() {
    //Test case code goes here

    ll n;
    cin >> n;

    map <ll, ll> b;
    ll sb = 0;

    for (ll i = 0; i < n + 2; ++i)
    {
        ll x;
        cin >> x;
        ++b[x];
        sb += x;
    }

    ll sa = -1;
    ll x = -1;

    bool notfound = true;

    for (auto &p : b) {
        if (p.ss <= 0) {
            continue;
        }
        sa = p.ff;
        x = sb - sa - sa;

        --b[sa];

        if (b[x]) {
            --b[x];
            notfound = false;
            break;
        }

        ++b[sa];
    }

    if (notfound) {
        cout << -1 << endl;
        return;
    }

    for (auto &p : b) {
        for (int i = 0; i < p.ss; ++i)
        {
            cout << p.ff << " ";
        }
    }

    cout << endl;
    return;

}

int main() {

    ios_base::sync_with_stdio(0);
    cin.tie(nullptr);
    cout.tie(nullptr);

    // Code goes here
    int t;
    cin >> t;
    // t = 1;

    while (t--) {
        solve();
    }

    return 0;
}