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:
for z in range (int(input())):
	n = int(input())
	a = list(map(int,input().split()))

	ma = a[0]
	mai = 0
	for i in range (n+2):
		if(a[i] > ma):
			ma = a[i]
			mai = i

	#print(ma,mai)
	su = sum(a) - ma
	#print(su)
	fl = 0
	i2 = -1
	for i in range (n+2):
		if(i!=mai and su-a[i]==ma):
			#print(i)
			fl=1
			i2 = i
			break

	if(fl == 0):
		#print("**")
		a.remove(ma)

		ma2 = a[0]
		ma2i = 0
		for i in range (n+1):
			if(a[i] > ma2):
				ma2 = a[i]
				ma2i = i

		if(sum(a)-ma2 == ma2):
			for i in range (n+1):
				if(i!=ma2i):
					print(a[i],end=" ")
			print()

		else:
			print(-1)

	else:
		for i in range (n+2):
			if(i!=i2 and i!=mai):
				print(a[i],end=" ")
		print()