Assume that a defendant is arrested in his kitchen for the armed robbery of a bank earlier that day. The arresting officers have an arrest warrant but no search warrant. The defendant is one of three persons wanted in the robbery. The defendant's automobile, the suspected getaway car, is parked in his driveway. In your post, indicate the full extent of the arresting officers' authority to search the defendant, his premises, and his automobile under the search-incident-to-a-lawful-arrest doctrine.