KöMaL 2018 B4942

The one hundred mathematicians participating in an international combinatorial conference were all housed in the same hotel. The receptionist was originally planning to place them in the order of their arrival in the rooms numbered 1 to 100. However, he forgot to give that instruction to the guest arriving first, who has thus chosen a room at random. So the receptionist instructed all the other guests to take the room with their number in the order of arrivals, or, if that room has already been taken, to select any other room they like. How many possible arrangements of the guests in the rooms are there?