Kitchen Cabinet Installation on drywall over cinder block wall.?

I would like to install some kitchen cabinets on a wall where drywall was installed over 1x 4 furring strips which were then attached to a cinder block wall. I am unsure on how to proceed. Will these strips along with the frame in the back of the cabinet be sufficient to support the weight of the cabinet and its contents? What type of screws should I use? How would you proceed with this installation?