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;
int n,b[200002];
signed main(){
	for(cin>>n;cin>>n;){
		long long s=0;int y,z;multiset<int>o;for(int i=0;i<n+2;i++)cin>>b[i],s+=b[i],o.insert(b[i]);y=*prev(o.end()),z=*prev(prev(o.end())),(s-=y)-=z,o.erase(o.find(y)),o.erase(o.find(z));
		if(s==y||s==z){
			for(auto v:o)cout<<v<<' ';cout<<endl;continue;
		}
		s+=z,o.insert(z);
		if(s-y<2e9&&o.find(s-y)!=o.end()){int f=1;
			for(auto v:o)if(!f||v-s+y)cout<<v<<' ';else if(v==s-y)f=0;cout<<endl;continue;
		}else{s-=z,o.erase(o.find(z)),s+=y,o.insert(y);
			if(s-z<2e9&&o.find(s-z)!=o.end()){int f=0;
				for(auto v:o)if(!f||v-s+z)cout<<v<<' ';else if(v==s-z)f=0;cout<<endl;continue;
			}
		else puts("-1");}
	}
}