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:
t=int(input())

def deleteonetime(b, x):
   r = b[:]
   for i in range(len(r)):
      if r[i] == x:
         return r[:i] + r[(i+1):]
   return r

def rep(b, n):
   S = sum(b)
   # find x, y in b such as y = S-x-y
   #mettre tous les 2y dans un dico
   #pour tout x, regarder si S-x dans dico, si oui content
   #sinon fail
   #Sinon remarquer si b est trie, y doit etre dans les 2 derniers
  
   dico = {}
   for y in b:
      if not 2*y in dico:
         dico[2*y] = 1
      else:
         dico[2*y] += 1
   for x in b:
      if (S-x) in dico and (dico[S-x] > 1 or (x != (S-x)//2)):
         a = b[:]
         y = (S-x)//2
         a = deleteonetime(a, y)
         return deleteonetime(a, x)
   return [-1]
for _ in range(t):
   n = int(input())
   a = list(map(int,input().split()))
   print(' '.join(map(str, rep(sorted(a), n))))