PA28 Flight Instructor reported a sudden loss of engine power during cruise. Flight instructor diverted to the nearest field and landed.

Narrative

I was instructing a checkride prep student. We were at 2;500 ft MSL performing steep turns followed by a quick simulated engine failure. After recovering from the simulated engine out; and while we were climbing back up to 2;500 there was a loud pop from the engine; sudden loss of power and the plane started shaking violently. we were at about 1;500 feet MSL at this point. I assumed control from my student; reduced power from full throttle to 2000 rpm. I then determined my home airport was 20 miles away; while there was a closer option 10 miles away on the other side of restricted airspace R-XXXX. At this point I contacted ZZZ Approach on XXX.XX; informed them I was experiencing an engine failure. I then informed them I was flying through restricted airspace to the closest airport; ZZZ. The airplane was unable to maintain altitude however; I was able to limp the airplane to ZZZ; landing straight in on Runway XX and then taxiing to the ramp. Upon after landing inspection; I determined the cause for the failure was a blown cylinder head. after landing I called ZZZ Approach to inform them we landed safely