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 find (x, sm):

    if sm % 2:
        return 0

    try:
        return cnt[sm // 2] > (x == sm // 2)
    except:
        return 0

def out(el, sm):

    t1 = t2 = 1

    for i in range(n + 2):
        if a[i] == sm and t1:
            t1 = 0
            continue
        elif a[i] == el and t2:
            t2 = 0
            continue
        else:
            print(a[i], end= " ")

    print()

def sol():

    global n, a, sum, cnt

    n = int(input())
    a = list(map(int, input().split()))
    a = list(sorted(a))

    sum = 0
    cnt = {}

    for i in range (n + 2):
        try:
            cnt[a[i]] += 1
        except:
            cnt[a[i]] = 1
        sum += a[i]

    for i in range (n + 2):
        if find(a[i], sum-a[i]):
            out(a[i], (sum-a[i])//2)
            return

    print(-1)

TN = int(input())

while TN != 0:
    sol()
    TN -= 1