Crash It

Roger recently built a circular race track with length $K$. After hosting a few races, he realised that people do not come there to see the race itself, they come to see racers crash into each other (what's wrong with our generation...). After this realisation, Roger decided to hold a different kind of "races": he hired $N$ racers (numbered $1$ through $N$) whose task is to crash into each other.