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"
#define ll long long
#define endl "\n"
using namespace std;
ll MOD = 998244353ll;
ll power(ll base,ll exp)
{
    base = base % MOD;
    if(base==0)
        return 0;
    if(exp==0)
        return 1;
    ll ans=1;
    ll temp = power(base,exp/2); 
    ans =  (temp * temp) % MOD;
    if(exp & 1)
        ans = (ans * base)%MOD;
    return ans;
}
ll inverse(ll a)
{
    return power(a,MOD-2);
}

void solve()
{
	int n;
    cin>>n;
    int b[n+2];
    ll sum =0;
    for(int i=0;i<n+2;i++)
    {
        cin>>b[i];
        sum+= b[i];
    }
    map<ll,int> mp;
    for(int i=0;i<n+2;i++)
    {
        mp[b[i]]++;
    }

    for(int i=0;i<n+2;i++)
    {

        ll y = sum - b[i];
        mp[b[i]]--;
        if(y%2==1)
        {
            mp[b[i]]++;
            continue;
        }
        if(mp.find(y/2)!=mp.end())
        {
            if(mp[y/2]>0)
            {
                // cout<<"ff";
                bool found = false;
                for(int j=0;j<n+2;j++)
                {
                    if(j==i)
                        continue;
                    else if(!found && b[j]==y/2)
                    {
                        found=true;
                    }
                    else
                        cout<<b[j]<<" ";
                }
                cout<<endl;
                return;
            }
        }
        mp[b[i]]++;
    }
    cout<<-1<<endl;return;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    // freopen("C:\\Users\\KAMLESH PRAJAPATI\\Desktop\\input.txt","r",stdin);
    // freopen("C:\\Users\\KAMLESH PRAJAPATI\\Desktop\\output.txt","w",stdout);
    int test;
    cin>>test;
    while(test--)
    {
        solve();
    }
    return 0;
}