It never occurred to me that appending am or pm to midday or midnight made no sense whatsoever. Am I the only one?
It took a Google Search and this Greenwich Meantime site for the penny to drop.
A.M. and P.M. start immediately after Midnight and Noon (Midday) respectively. This means that 00:00 A.M. or 00:00 P.M. (or 12:00 A.M. and 12:00 P.M.) have no meaning.