AMC 12 2016b Problem 10

A quadrilateral has vertices $P(a,b)$, $Q(b,a)$, $R(-a, -b)$, and $S(-b, -a)$, where $a$ and $b$ are integers with $a>b>0$. The area of $PQRS$ is $16$. What is $a+b$?

\textbf{(A)}\ 4 \textbf{(B)}\ 5 \textbf{(C)}\ 6 \textbf{(D)}\ 12 \textbf{(E)}\ 13