Middle European Mathematical Olympiad 2023 Problem I-2

Find all integers $n \geq 3$ for which it is possible to draw $n$ chords of one circle such that their $2n$ endpoints are pairwise distinct and each chord intersects precisely $k$ other chords for:

(a) $k = n - 2$,

(b) $k = n - 3$.

Remark. A chord of a circle is a line segment whose both endpoints lie on the circle.