TH-TMO 2019 Problem 4

A rabbit initially stands at the position $0$ , and repeatedly jumps on the real line. In each jump, the rabbit can jump to any position corresponds to an integer but it cannot stand still. Let $N(a)$ be the number of ways to jump with a total distance of $2019$ and stop at the position $a$ . Determine all integers $a$ such that $N(a)$ is odd.