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 max_list(int_list):

    max = 0
    second_max = 0
    sum = 0
    for i in range(len(int_list)):
        sum = sum + int_list[i]
        if (int_list[i] > max):
            second_max = max
            max = int_list[i]
        elif (int_list[i] > second_max):
            second_max = int_list[i]


    return max,second_max, sum

def count_element(elem,l):

    counter = 0
    for i in range(len(l)):
        if (l[i] == elem):
            counter = counter + 1

    return counter

t = int(input())

for i in range(t):

    flag = 0

    n = int(input())
    list_A = list(map(int, input().strip().split(' ')))

    max,second,sum = max_list(list_A)

    first_candidate = sum - max
    second_candidate = sum - second

    num1 = first_candidate - max

    num2 = second_candidate - second


    if (num1 in list_A and (num1 != max or count_element(num1,list_A) > 1) and flag == 0):
        list_A.remove(num1)
        list_A.remove(max)
        flag = 1


    if (num2 in list_A and (num2 != second or count_element(num2,list_A) > 1) and flag == 0):
        list_A.remove(num2)
        list_A.remove(second)
        flag = 1


    if (flag == 1):
        for i in range(len(list_A)):
            print(list_A[i],end= ' ')
        print()
    else:
        print(-1)