BALTIC-WAY 2004 Problem 19

$D$ is the midpoint of the side $B C$ of the given triangle $A B C . M$ is a point on the side $B C$ such that $\angle B A M=\angle D A C$. $L$ is the second intersection point of the circumcircle of the triangle $C A M$ with the side $A B . K$ is the second intersection point of the circumcircle of the triangle $B A M$ with the side $A C$. Prove that $K L \| B C$.