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 w in range(int(input())):
    n = int(input())
    b = list(map(int,input().split()))
    # print(b)
    b = sorted(b)
    ans = 0
    m = n+2
    x = b[m-1]
    a = []
    temp_sum = 0
    for i in range(m-1):
        temp_sum+=b[i]
    for i in range(m-1):
        if(temp_sum - b[i] == x):
            ans = 1
            for j in range(m-1):
                if(j!=i):
                    a.append(b[j])
            break
    if(ans==0):
        temp_sum_2 = 0
        for i in range(m-2):
            temp_sum_2 += b[i]
        if(b[-2]==temp_sum_2):
            ans = 1
            for i in range(m-2):
                a.append(b[i])
             
    if(ans==0):
        print(-1)
    else:
        for i in range(n):
            print(a[i],end=" ")
        print()
    # if(n==1):
    #     print("YES")
    #     if(b.count(b[0])==2):
    #         print(b[0])
    #     elif(b.count(b[1])==2):
    #         print(b[1])
    #     elif(b.count(b[2])==2):
    #         print(b[2])
    #     else:
    #         print(-1)
    # elif(n==2):
    #     if(b[2]==b[0]+b[1]):
    #         print(b[0],b[1])
    #     elif(b[-1]==b[0]+b[1]):
    #         print(b[0],b[1])
    #     elif(b[-1]==b[0]+b[2]):
    #         print(b[0],b[2])
    #     elif(b[-1]==b[1]+b[2]):
    #         print(b[1],b[2])
    #     else:
    #         print(-1)
    # print(b)