2010 AMC 12A Problem 18

A 16-step path is to go from (-4,-4) to (4,4) with each step increasing either the x-coordinate or the y-coordinate by 1. How many such paths stay outside or on the boundary of the square -2 \le x \le 2, -2 \le y \le 2 at each step?

\textbf{(A)}\ 92 \qquad \textbf{(B)}\ 144 \qquad \textbf{(C)}\ 1568 \qquad \textbf{(D)}\ 1698 \qquad \textbf{(E)}\ 12,800

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