IZhO 2006 Problem 2

Let $ABC$ be a triangle and $K$ and $L$ be two points on $(AB)$ , $(AC)$ such that $BK = CL$ and let $P = CK\cap BL$ . Let the parallel through $P$ to the interior angle bisector of $\angle BAC$ intersect $AC$ in $M$ . Prove that $CM = AB$ .