XOR Subsequence

Alice used to have a sequence $a_1,\cdots,a_n$, but she has forgotten about it now. Fortunately, she noticed that she had calculated the XOR sum for each non-empty subsequence of the sequence and obtained $2^n-1$ results, but their order was disrupted.

Now she hopes you can help restore the sequence. If there are multiple possible sequences, please tell her the sequence with the **smallest lexicographical order**, or report there is no correct sequence.

The first line contains a single integer $T$ ($1\le T\le 5000$), denoting the number of test cases.

For each test case, the first line contains an integer $n$ ($1\le n\le 18$).

The next line contains $2^n-1$ non-negative integers strictly less than $2^{30}$, denoting the results.

It is guaranteed that the sum of $2^n$ over all test cases does not exceed $2^{20}$.

For each test case, output one line. If there is no correct sequence, output $-1$; otherwise, output $n$ integers denoting the answer.

3
3
1 2 3 4 5 6 7
3
1 0 1 0 1 0 1
3
1 2 3 4 5 6 6

1 2 4
0 0 1
-1

2023“钉耙编程”中国大学生算法设计超级联赛（10）