If the coefficients of $x^3$ and $x^5$ in the expansion of $(1+ax+bx^2)(1-2x)^{18}$ in powers of $x$ are both zero, then $(a,b)$ is equal to:

Question

$\begin{array}{1 1} (A) (16, \large\frac{251}{3}) \\ (B) (14, \large\frac{251}{3}) \\ (C) (14, \large\frac{272}{3}) \\ (D) (16, \large\frac{272}{3}) \end{array}$