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 ll long long
void ans(ll int a[],ll int n){
	sort(a,a+n);
	ll int n1 = n-2 , s=0 , p = a[n-1];
	set <ll int> st; // has the difference.
	for(ll int i=0;i<n1;i++) s += a[i];

	if(s > p) {
		// no ans
		cout << "-1";
		return;
	}

	if(s == a[n1]){
		// ans
		for(ll int i=0;i<n1;i++){
			cout << a[i] << " ";
		}
		return;
	}	
	if(s == a[n-1]){
		// ans
		for(ll int i=0;i<n1;i++){
			cout << a[i] << " ";
		}
		return;
	}

	ll int x = a[n-2];
	for(ll int i=0;i<n1;i++)
		st.insert(x - a[i]); // difference arr

		std::vector<ll int> v;
	
		ll int y = p - s;
		if(st.find(y) != st.end()){
				//ans.
			for(ll int i=0;i<n1;i++)
			{
				s = s - a[i];
				s = s + x;
				if(s == p)
				{
					for(ll int k=0;k<n1;k++)
					{
						if(k==i){
							v.push_back(x);
						}
						else v.push_back(a[k]);
					}
					sort(v.begin(),v.end());
					for(ll int x : v)
						cout << x << " ";
					return;
				}
				s = s - x;
				s = s + a[i];
			}
		 
		}	

		else {
			// no ans
			cout << "-1";
			return;
		}
	
}
int main(){
	ios_base::sync_with_stdio(false);
    cin.tie(NULL);
	ll int t;
	cin >> t;
	while(t--){
		ll int n1;
		cin >> n1;
		ll int n = n1+2;
		ll int a[n];
		for(ll int i=0;i<n;i++)
			cin >> a[i];
		ans(a,n);
		cout << '\n';
	}
}