2011 AMC 12B 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 \qquad \textbf{(B)}\ 185 \qquad \textbf{(C)}\ 195 \qquad \textbf{(D)}\ 227 \qquad \textbf{(E)}\ 255

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.