MK-MO 2016 Problem 4

A segment $AB$ is given and it's midpoint $K$ . On the perpendicular line to $AB$ , passing through $K$ a point $C$ , different from $K$ is chosen. Let $N$ be the intersection of $AC$ and the line passing through $B$ and the midpoint of $CK$ . Let $U$ be the intersection point of $AB$ and the line passing through $C$ and $L$ , the midpoint of $BN$ . Prove that the ratio of the areas of the triangles $CNL$ and $BUL$ , is independent of the choice of the point $C$ .