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.