KMO 2015 Problem 2

Let the circumcircle of $\triangle ABC$ be $\omega$ . A point $D$ lies on segment $BC$ , and $E$ lies on segment $AD$ . Let ray $AD \cap \omega = F$ . A point $M$ , which lies on $\omega$ , bisects $AF$ and it is on the other side of $C$ with respect to $AF$ . Ray $ME \cap \omega = G$ , ray $GD \cap \omega = H$ , and $MH \cap AD = K$ . Prove that $B, E, C, K$ are cyclic.