Boring Game

Problem Description

Given $n$ sheets of paper, place them on the table in pile and fold them in half $k$ times from left to right. Now from top to bottom, mark a number on paper at each side of the front and back. So there are $2 \times n \times 2^k$ numbers in total and these numbers form a permutation $P$. Now it expands to its original. These numbers from top to bottom, from front to back, from left to right form a permutation $Q$. Given the permutation $P$, find the permutation $Q$. See example for details. For $k=1$ and $P=1..4 \times n$, you can assume that you are marking the page numbers before printing a booklet forming from $n$ pieces of $A4$ papers.

Input

The first line contains a single integer $T(1 \leq T \leq 30)$ , the number of test cases. For each test case, the first line gives two integers $n$, $k$($1 \leq n \leq 200, 1 \leq k \leq 10$). The next line gives the permutation $P$ that consists of $2 \times n \times 2^k$ integers $p_i(1 \leq p_i \leq 2 \times n \times 2^k)$. It is guaranteed that $\sum 2 \times n \times 2^k$ doesn't exceed $10^6$.

Output

The output should contain $T$ lines each containing $2 \times n \times 2^k$ integers separated by spaces, indicating the permutation $Q$.

Sample Input

1
2 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Sample Output

12 5 4 13 11 6 3 14 10 7 2 15 9 8 1 16
[hint]
[center][img]../../data/images/C883-1003-1.png[/img][/center]
[\hint]

Source

2020 Multi-University Training Contest 5