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 forever         while(true)
#define int             long long
#define rep(i, s, n)    for(int i=s;i<n;i++)
#define fo(i, n)        rep(i, 0, n)
#define tr(c, it)       for(auto it : c)
#define all(c)          (c).begin(), (c).end()
#define sz(x)           (int)(x.size())
#define ff              first
#define ss              second
#define pb              push_back
#define ppb             pop_back
#define pf              push_front
#define ppf             pop_front
#define uniq(v)         (v).erase(unique(all(v)),(v).end())
#define mp              make_pair
#define pii             pair<int,int>
#define vi              vector<int>
#define mii             map<int,int>
#define pqb             priority_queue<int>
#define pqs             priority_queue<int,vi,greater<int> >
#define mem1(a)         memset(a,-1,sizeof(a))
#define mem0(a)         memset(a,0,sizeof(a))
#define w(x)            int x; cin>>x; while(x--)
#define ppc             __builtin_popcount
#define ppcll           __builtin_popcountll


const long long INF = 1e18;
const int32_t M = 1e9 + 7;
const int32_t MM = 998244353;
const int N = 1e9 + 1;


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

    vi v(n + 2);
    int sum = 0;

    rep(i, 0, n + 2) {
        cin >> v[i];
        sum += v[i];
    }

    sort(all(v));

    int gr1 = v[n + 1];
    int gr2 = v[n];

    int b = -1, c = -1;
    int s;

    rep(i, 0, n + 2) {

        if (i == n + 1) {
            s = sum - gr1;
            if (s == 2 * gr2) {
                b = gr2;
                c = gr1;
            }
        }

        else {
            s = sum - v[i];
            if (s == 2 * gr1) {
                b = gr1;
                c = v[i];
            }

        }

    }

    if (b == -1) {
        cout << "-1\n";
    }

    else {
        rep(i, 0, n + 2) {
            if (v[i] == b) {
                b = -1;
                continue;
            }

            if (v[i] == c) {
                c = -1;
                continue;
            }

            cout << v[i] << " ";
        }
        cout << "\n";
    }
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
#ifdef SIEVE
    sieve();
#endif
#ifdef NCR
    init();
#endif
    w(t) solve();
    return 0;
}