They would have felt sorry for Hagrid when the time came for him to say good-bye to Norbert if they hadn't been so worried about what they had to do. It was a very dark, cloudy night, and they were a bit late arriving at Hagrid's hut because they'd had to wait for Peeves to get out of their way in the entrance hall, where he'd been playing tennis against the wall. (Harry Potter and the Sorcerer's Stone)
It seems that ‘late’ is complementized far more with ‘arriving’[A] than ‘to arrive’[B]. What’s the difference between the two in meaning?