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 PYTHON3):

Solution:
ll=lambda:map(int,input().split())
t=lambda:int(input())
ss=lambda:input()
lx=lambda x:map(int,input().split(x))
from math import log10 ,log2,ceil,factorial as fac,gcd
#from itertools import combinations_with_replacement as cs 
#from functools import reduce
#from bisect import bisect_right as br,bisect_left as bl
#from collections import Counter
#from math import inf
 
 
for _ in range(t()):

    
    n=t()
    b=list(ll())

    nb=n+2

    a=sorted(b)

    x=a[:n]
    s=sum(x)

    if s in a[n:]:
        print(*x)
        continue
    fi,sec=a[-1],a[-2]

    for i in range(n):
        if s-x[i]+sec==fi:
            x[i]=sec
            print(*x)
            break
        elif s-x[i]+fi==sec:
            x[i]=fi
            print(*a)
            break
    else:
        print(-1)
            
    

        
        

    

    

    

    
    
    
#f()