Circle of Chaos

You are an evil sorcerer at a round table with $N$ sorcerers (including yourself). You can cast $M$ spells which have distinct powers $p_1, p_2, \ldots, p_M$. You may perform the following operation any number of times (possibly zero): - Assign a living sorcerer to each positive integer cyclically to your left starting from yourself ― the closest living sorcerer to your left is assigned to $1$, t