Winner Winner Cupcake Dinner

Its dinner time and cupcakes are on the menu. L and Light are at the dinner table. To make things interesting, L challenges Light to a fun game. The cupcakes are labelled $1$ to $N$ and are in a circle on the round table. The game is played in alternate turns. The game starts at the $K^{th}$ cupcake, here $K$ is decide by L. At any turn, the player picks the cupcake and eats it. Now the next playe