13216번 - Badminton

Anisa (Player A) and Ben (Player B) are playing a singles badminton match. Here are the basic badminton rules:

• To win a match, a player needs to win 2 out of 3 games.
• The first player to reach 21 points wins the game. (A different rule applies when the players are tied 20-20. You may assume this case does not happen.)
• Either player can score a point no matter who serves.
• After a game is won, a new game begins and the score resets to 0-0.

A sequence of A’s and B’s that records which player scored for each serve.

The score and who wins the match (A or B).