CF1512D.Corrupted Array

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.

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 $2 \cdot 10^5$ .

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.