Complex sentence: "Birthday" was written by Perry, Bonnie McKee, Cirkut, Dr. Luke and Max Martin, while its production was helmed by the latter three, who also contributed to the instrumentation and programmed their respective instruments.
Split into simpler sentences: Birthday was written by Perry, Bonnie McKee, Cirkut, Dr. Luke, and Max Martin. The latter three produced the song and contributed to the instrumentation and programmed their respective instruments.