UA-UMO 1999 Problem 102

Let $M$ be a point inside a triangle $ABC$ . The line through $M$ parallel to $AC$ meets $AB$ at $N$ and $BC$ at $K$ . The lines through $M$ parallel to $AB$ and $BC$ meet $AC$ at $D$ and $L$ , respectively. Another line through $M$ intersects the sides $AB$ and $BC$ at $P$ and $R$ respectively such that $PM=MR$ . Given that the area of $\triangle ABC$ is $S$ and that $\frac{CK}{CB}=a$ , compute the area of $\triangle PQR$ .