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:
from collections import Counter, defaultdict
import sys
def get_ints(): return list(map(int, sys.stdin.readline().strip().split()))

def solve(target_N, nums):
    total = 0
    # vis = defaultdict(int)
    vis = Counter(nums)
    max_val, sec_max = -1, -1
    nums.sort()
    max_val, sec_max = nums[-1], nums[-2]
    total = sum(nums)
    # for i in range(len(nums)):
    #     vis[nums[i]] += 1
    #     total += nums[i]
    #     if nums[i] >= max_val:
    #         sec_max = max_val
    #         max_val = nums[i]

    vis[max_val] -= 1
    temp_total = total - max_val
    target = temp_total - max_val
    if target in vis and vis[target] > 0:
        ans = []
        vis[target] -= 1
        # print(target, temp_total, max_val)
        # print(vis)
        for v in vis:
            if vis[v] > 0:
                ans += [str(v)] * vis[v]
        return (" ").join(ans)
    vis[max_val] += 1

    vis[sec_max] -= 1
    temp_total = total - sec_max
    target = temp_total - sec_max
    if target in vis and vis[target] > 0:
        ans = []
        vis[target] -= 1
        for v in vis:
            if vis[v] > 0:
                ans += [str(v)] * vis[v]
        return (" ").join(ans)

    return -1

T = int(input())
for _ in range(T):
    target_N = int(input())
    nums = get_ints()
    print(solve(target_N, nums))