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;
///////////////////////////////////*****************//////////////////////////////////////
typedef long long ll;
ll z=1000000007;
ll fact[400005];
void buildfact()
{
    fact[0]=1;
    for(ll i=1;i<400005;i++)
    {
        fact[i]=(fact[i-1]*i)%z;
    }
}
ll power(ll a,ll p)
{
    if(p==0)
        return 1;
    if(p%2==0)
        return power((a*a)%z,p/2);
    return (a*power(a,p-1))%z;
}
ll ncr(ll n,ll r)
{
    if(n<r)
        return 0;
    ll num=fact[n];
    ll deno=(fact[r]*fact[n-r])%z;
    deno=power(deno,z-2);
    ll ans=(num*deno)%z;
    return ans;
}
//////////////////////////////////////****************//////////////////////////////////////

void solve(int oper)
{
ll n;
cin>>n;
ll arr[n+2];
for(int i=0;i<n+2;i++)
    cin>>arr[i];
sort(arr,arr+n+2);
int skip=-1;
ll sum=0;
for(int i=0;i<n+1;i++)
{
   sum+=arr[i];
}
if(sum-arr[n]==arr[n])
{
    for(int i=0;i<n;i++)
        cout<<arr[i]<<" ";
    cout<<endl;
    return;
}
for(int i=0;i<n+1;i++)
{
    if(sum-arr[i]==arr[n+1])
        skip=i;
}
if(skip==-1)
{
    cout<<-1<<endl;
    return;
}
for(int i=0;i<n+1;i++)
{
    if(i!=skip)
    {
        cout<<arr[i]<<" ";
    }
}
cout<<endl;
return ;
}
int main()
{
    ll t;
    t=1;
    cin>>t;
   //buildfact();
    int i=1;
    while(i<=t)
    {
        solve(i);
        i++;
    }
    return 0;
}