TR-MO-R1 2017 Problem 29

$\binom{2017}{1}+\binom{2017}{5}+\binom{2017}{9}+\binom{2017}{13}+\cdots+\binom{2017}{2013}+\binom{2017}{2017}=?$

A) $2^{2016}+2^{1006}$ B) $2^{2017}-2^{1007}$ C) $2^{2015}+2^{1005}$ D) $2^{2015}+2^{1007}$ E) $2^{2017}-2^{1008}$