VN TST 1997 Question 6

Let $n,k,p$ be positive integers with $k\ge2$ and $k(p+1)\le n$. There are $n$ distinct fixed points on a circle. Color every point either blue or red so that exactly $k$ points are blue and every clockwise arc between consecutive blue points contains at least $p$ red points. How many different colorings are there? Two colorings are different if at least one fixed point has different colors in them.

The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.