Corrupted Array

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

inputFormat

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.

outputFormat

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

样例

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

2 3 7
-1
2 2 2 3 9
1 2 6

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