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 unsigned long long int ull;
typedef long long int ll;
typedef long double ld;
#define fr(i,a,b) for(ll i=a; i<b; i++)
#define rf(i,a,b) for(ll i=a; i>=b; i--)
#define pb push_back
#define mp make_pair
#define show(a) for(auto el:a)cout<<el<<" "
#define ff first
#define ss second
#define pairv vector<pair<ll,ll>>
#define vec vector <ll> 
#define all(a) a.begin(),a.end()
#define fam(v,i) for(auto i=v.begin();i!=v.end();i++)
#define fai(v,i) for(auto i : v)
#define mo 1000000007
#define nn cout<<"\n";
#define Y cout<<"YES\n";
#define N cout<<"NO\n";
#define cout_dec cout << fixed << setprecision(9) 
#define casepr(ti)  cout<<"case #"<<ti+1<<": "
#define fill(a,b) memset(a, b, sizeof(a))
ll pow1(ll n,ll p)
{
if(p==0) return 1; 
ll x=pow1(n, p/2);
x=(x*x)%mo;
if(p%2==0)
return x;
else
return (x*n)%mo;
}
bool sortbysec(const pair<ll,ll> &a, 
const pair<ll,ll> &b) 
{ 
return (a.second < b.second); 
} 
bool compare(const pair<ll, ll>&p1, const pair<ll,ll>&p2)
{
if(p1.ff < p2.ff) return true;
if(p1.ff == p2.ff) return p1.ff < p2.ss;
return false;
}
ll const maxn=200007;
ll nxt[maxn];
void seive()
{
      for (ll i = 2; i < maxn; ++i) {
        if (nxt[i] == 0) {
            nxt[i] = i;
            for (ll j = i * i; j < maxn; j += i) {
                if(j>=maxn)
                {
                    break;
                }
                if (nxt[j] == 0) nxt[j] = i;
            }
        }
    }
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    int test=1;
    cin>>test;
    for(int ti=0;ti<test;ti++)
    {
        ll i,j,k,e,f,n,c=0,x=0;
        cin>>n;
        ll m=n+2;
        ll b[n+2];
        fr(i,0,n+2)
        cin>>b[i];
        sort(b,b+m);
        fr(i,0,n)
        {
            c=c+b[i];
        }
        if(c== b[n] || c==b[n+1])
        {
            fr(i,0,n)
            {
                cout<<b[i]<<" ";

            }
                            nn
                continue;
        }
        x=-1;
        fr(i,0,n)
        {
            if(c-b[i]+b[n]==b[n+1])
            {
                x=i;
                break;
            }
        }
        if(x==-1)
        {
            cout<<-1;
            
        }
        else
        {
            fr(i,0,n+1)
            {
                if(i==x)
                {
                    continue;
                }
                cout<<b[i]<<" ";
            }
        }
        
    

        
     nn
        
    }
    
     return 0;
}