KöMaL 2005 K47

There are two kinds of people living on an island: the good and the bad. The good always tell the truth and the bad always lie. Naturally, every inhabitant of the island is either a boy or a girl. Here is a conversation of two young people on the island: $A$: If I am good, $B$ is bad.'' $B$: If I am a boy, $A$ is a girl.'' Find out if each of them is good or bad and what sex they belong to.