Catch the Thief

A policeman wants to catch a thief. Both the policeman and the thief can only move on a line on integer coordinates between $0$ and $N$ (inclusive). Initially, the policeman is at a coordinate $x$ and the thief is at a coordinate $y$. During each second, each of them must move to the left or right (not necessarily both in the same direction) by distance $\textbf{exactly}$ equal to $K$. No one m