KZ-MO 2017 Problem 4

The acute triangle $ABC$ $(AC> BC)$ is inscribed in a circle with the center at the point $O$ , and $CD$ is the diameter of this circle. The point $K$ is on the continuation of the ray $DA$ beyond the point $A$ . And the point $L$ is on the segment $BD$ $(DL> LB)$ so that $\angle OKD = \angle BAC$ , $\angle OLD = \angle ABC$ . Prove that the line $KL$ passes through the midpoint of the segment $AB$ .