A Puzzle and a Solution

Let’s say we have a number $N$ of children placed in a circle and playing the following simple game: proceeding around the circle they kick out every $P$th of them (of course, $P < N$).

Of course, what we will obtain is a permutation of the first $N$ natural numbers. The puzzle asks for the order of this permutation (that is the number of times it must be applied to itself to get back to an ordered list.