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:
# Uses python3
from sys import stdin, stdout 
import sys
import math
import itertools
from collections import defaultdict
sys.setrecursionlimit(10**6)

def solve(arr):
	#max number has to be guessed or sum of others
	g = max(arr)
	maxi = arr.index(g)
	m = set()
	summation = sum(arr)-g

	for i in arr:
		m.add(i)
	ans = -1
	for i in range(len(arr)):
		if i!=maxi and summation-arr[i]==g:
			ans = (g,arr[i])
			break
	
	for i in range(len(arr)):
		if i!=maxi and summation-arr[i]==arr[i]:
			ans = (arr[i],g)
			break

	return ans

	



def main(): 
	t = int(stdin.readline().strip())
	for i in range (1,t+1):
		n = int(stdin.readline().strip())
		arr = [int(x) for x in stdin.readline().split()] 
		ans = solve(arr)
		if ans==-1:
			stdout.write('-1\n') 
		else:
			flag1=flag2=0
			for j in arr:
				if j==ans[0] and flag1==0:
					flag1=1
					continue
				if j==ans[1] and flag2==0:
					flag2=1
					continue

				print(j,end=" ")
			print()


# call the main method 
if __name__ == "__main__": 
	main()