D. Corrupted Array
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a number $n$ and an array $b_1, b_2, \ldots, b_{n+2}$, obtained according to the following algorithm:

• some array $a_1, a_2, \ldots, a_n$ was guessed;
• array $a$ was written to array $b$, i.e. $b_i = a_i$ ($1 \le i \le n$);
• The $(n+1)$-th element of the array $b$ is the sum of the numbers in the array $a$, i.e. $b_{n+1} = a_1+a_2+\ldots+a_n$;
• The $(n+2)$-th element of the array $b$ was written some number $x$ ($1 \le x \le 10^9$), 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 $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$).

The second row of each test case contains $n+2$ integers $b_1, b_2, \ldots, b_{n+2}$ ($1 \le b_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output:

• "-1", if the array $b$ could not be obtained from any array $a$;
• $n$ integers $a_1, a_2, \ldots, a_n$, 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