2022 Pascal Problem 18

Five balls, numbered 1 to 5, are placed in order on a table. A sequence of steps is performed on the balls. In step 1, the rightmost ball is picked up and put in the middle of the four remaining balls. (The remaining balls are shifted to make room for the inserted ball.) Then in step 2, the leftmost ball is picked up and put in the middle of the four remaining balls. These steps repeat, with the rightmost and leftmost balls alternately picked up and put in the middle of the four remaining balls. Immediately after step N, the balls are in the reverse of their original order. Which of the following is a possible value of N?

\textbf{(A)}\ 2020\quad \textbf{(B)}\ 2028\quad \textbf{(C)}\ 2031\quad \textbf{(D)}\ 2027\quad \textbf{(E)}\ 2025

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.