AMC 12 2010a 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 \textbf{(B)}\ 144 \textbf{(C)}\ 1568 \textbf{(D)}\ 1698 \textbf{(E)}\ 12,800