Statement

There are M tram stations arranged in a circle, numbered from 1 to M. There are N players, numbered from 0 to N-1, who wish to participate in a round-robin rock-paper-scissors tournament. Each player aims to play against every other player exactly once. However, two players can only play if they are at the same station. At the start, each player selects a station and purchases a ticket that permits them to move either clockwise or counterclockwise. The ticket remains valid throughout the tournament. Each minute, all players simultaneously move to the next station in the direction specified by their ticket. This movement happens instantaneously around the circle. Following a movement (or initially), players who meet at the same station engage in a match. If two players meet again later, they do not play another match. You are required to answer two questions: (1) [A)] How many matches will be played in total? (2) [B)] At what time does the last possible match occur?