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 solve_problem(n, data):
    sarr = sorted(data)
    s = sum(sarr[:-2])
    if s > sarr[-2] and s > sarr[-1]:
        return [-1]
    elif s == sarr[-1]:
        return sarr[:-2]
    elif s == sarr[-2]:
        return sarr[:-2]
    # must be last one as the previous one is a part of array
    sc = s + sarr[-2]
    s = sarr[-1]
    for i in range(len(sarr) - 1):
        # assume i is the random
        if sc - sarr[i] == s:
            return sarr[:i] + sarr[i+1:-1]
    return [-1]


def solve():
    t = int(input())
    for i in range(0, t):
        n = int(input())
        layers = input()
        ais = [int(x) for x in layers.split()]
        result = solve_problem(n, ais)
        for x in result:
            print(x, end=' ')
        print()


if __name__ == '__main__':
    solve()