Triangle ABC has \angle A = 90^\circ, AB = 2, and AC = 4. Circle \omega_1 has center C and radius CA, while circle \omega_2 has center B and radius BA. The two circles intersect at point E, different from point A. Point M is on \omega_2 and in the interior of ABC, such that BM is parallel to EC. Suppose EM intersects \omega_1 at point K and AM intersects \omega_1 at point Z. What is the area of quadrilateral ZEBK?