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:
def main():
    from sys import stdin, stdout

    for _ in range(int(stdin.readline())):
        n = int(stdin.readline())
        arr = list(map(int,stdin.readline().split()))
        arrsum = sum(arr)
        mydict = {}
        for i in range(len(arr)):
            if arr[i] in mydict:
                mydict[arr[i]].append(i)
            else:
                mydict[arr[i]] = [i]
        #print(mydict)
        flag = False
        tempx, tempsum = None, None
        for i in range(len(arr)):
            left = arrsum - arr[i]
            #print(left,i)
            if left%2 == 0 and len(mydict.get(left//2,[])) and  ((arr[i]!=left//2)or (arr[i]==left//2  and len(mydict[arr[i]])>1)):
                tempx = i
                tempsum = left//2
                flag = True

        if flag:
            mydict[arr[tempx]] = mydict[arr[tempx]][1:]
            mydict[tempsum] = mydict[tempsum][1:]

            for i in mydict:
                for _ in range( len(mydict[i]) ):
                    stdout.write(str(i)+' ')
            stdout.write('\n')
                    

        else:
            stdout.write('-1\n')

        



if __name__=='__main__':
    main()