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:
class Solution:
    def solve(self, n, b):
        m = n + 2
        b.sort()

        summ = sum(b[:m-1])
        largest = b[m-1]
        largest2 = b[m-2]

        for i in range(m-1):
            if summ - b[i] == largest:
                return self.return_arr(i, b, 1, m)

        if summ - largest2 == largest2:
            return " ".join([str(b[i]) for i in range(m-2)])

        return -1

    def return_arr(self, i, b, k, m):
        return " ".join([str(b[j]) for j in range(m-k) if j != i])


if __name__ == '__main__':
    sol = Solution()
    tests = int(input())
    results = []
    for _ in range(tests):
        n = int(input())
        b = list(map(int, input().split()))
        result = sol.solve(n, b)
        results.append(result)

    for result in results:
        print(result)