AMC 12 2011b Problem 23

A bug travels in the coordinate plane, moving only along the lines that are parallel to the $x$-axis or $y$-axis. Let $A = (-3, 2)$ and $B = (3, -2)$. Consider all possible paths of the bug from $A$ to $B$ of length at most $20$. How many points with integer coordinates lie on at least one of these paths?

\textbf{(A)}\ 161 \textbf{(B)}\ 185 \textbf{(C)}\ 195 \textbf{(D)}\ 227 \textbf{(E)}\ 255