2018 Fermat Problem 20

For how many positive integers x is (x-2)(x-4)(x-6)\cdots(x-2016)(x-2018) \le 0? (The product on the left side of the inequality consists of 1009 factors of the form x-2k for integers k with 1 \le k \le 1009.)

\textbf{(A)}\ 1009\quad \textbf{(B)}\ 1010\quad \textbf{(C)}\ 1514\quad \textbf{(D)}\ 1515\quad \textbf{(E)}\ 1513

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.