BALKAN 2018 Problem 1

A quadrilateral $A B C D$ is inscribed in a circle $k$, where $A B>C D$ and $A B$ is not parallel to $C D$. Point $M$ is the intersection of the diagonals $A C$ and $B D$ and the perpendicular from $M$ to $A B$ intersects the segment $A B$ at the point $E$. If $E M$ bisects the angle $C E D$, prove that $A B$ is a diameter of the circle $k$.