Rally Scoreboard

Turn a rally-by-rally log of a table-tennis match into the game scores and the current status, including who serves next.

Two players, A and B, play a match. A game is won by the first player to reach target points and lead by at least 2, so at target - 1 each the game continues until someone is two ahead (for example, with target = 11, the scores 11-9 and 14-12 end a game, but 11-10 does not). target is always odd.

A match is the best of games games (games is odd): the first player to win games // 2 + 1 games wins the match. Once the match is won, any remaining rallies in the log are ignored.

Serving. The player who serves first in game 1 is given. The first server alternates every game: the opposite player serves first in game 2, and so on. Within a game, the serve changes hands every 2 rallies (the first server serves rallies 1 and 2, the other player rallies 3 and 4, and so on). Once both players have at least target - 1 points, the serve changes after every rally instead, continuing from whoever is next to serve.

Input: target; games; first_server, "A" or "B"; rallies, a string of "A" and "B" letters, the winner of each rally in order.

Output: a list of strings. First, one string "x-y" for each finished game in order, where x is A's points and y is B's. Then one final status string:

• if the match has been won: "MATCH <winner> <games won by the winner>-<games won by the loser>", for example "MATCH A 3-1";
• otherwise: "LIVE <A's games>-<B's games> <A's points>-<B's points> <next server>" describing the unfinished game and who serves the next rally. If a game has just finished, the unfinished game is the next one, at 0-0, with its first server as next server.