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 FASTIO	ios_base::sync_with_stdio(false),cin.tie(NULL),cout.tie(NULL)
#define ll long long 
#define mset(A,val) memset(A,val,sizeof(A))
#define fi(a,b) for(int i=a;i<=b;++i)
#define fj(a,b) for(int j=a;j<=b;++j)
#define all(x) x.begin(),x.end()
#define vi vector<int>
#define pii pair<int,int>
#define eb emplace_back
#define DEBUG(a...) cout<<#a<<": ";for(auto &it:a)cout<<it<<" ";cout<<"\n";
#define debug(a)cout<<#a<<": "<<a<<"\n";
#define int long long

// ---------------------------------------------------------------------------
const int mod = 1e9+7;
const int maxn = 2e5 + 9;

// ---------------------------------------------------------------------------
void init(){}

// ---------------------------------------------------------------------------
void test_case(int tc)
{
    // cout<<"Case #"<<tc<<": ";
    init();
    int n;cin>>n;
    n+=2;
    int totSum = 0;
    vi arr(n);fi(0,n-1)cin>>arr[i],totSum+=arr[i];
    sort(all(arr));
    // last element is sum of all 
    int sum = arr[n-1];
    int ans = -1;
    fi(0,n-2){
        if(totSum-sum-arr[i]==sum){
            ans = arr[i];
            fj(0,n-2){
                if(i!=j){
                    cout<<arr[j]<<" ";
                }
            }
            cout<<"\n";
            return;
        }
        
    }
    sum = arr[n-2];
    ans = -1;
    fi(0,n-1){
        if(i==n-2)continue;
        if(totSum-sum-arr[i]==sum){
            ans = arr[i];
            fj(0,n-1){
                if(i!=j && j!=n-2){
                    cout<<arr[j]<<" ";
                    
                }
            }
            cout<<"\n";
                return;
        }
        
    }
    cout<<"-1\n";
}

int32_t main()
{
    FASTIO;
    #ifndef ONLINE_JUDGE
         freopen("input.txt","r",stdin);
         // freopen("output.txt","w",stdout);
    #endif
    
    int t=1;
    cin>>t;
    for(int tc=1;tc<=t;++tc)test_case(tc);
}