Statement

You are attending a table tennis tournament and you decided to note down the results the players achieved. However, a bad misfortune happened and you lost your detailed list of results so you don't know the way the games went anymore. There is good news though: In order to avoid a complete loss of data, you also noted how many points each player has scored in total during all the sets they played. In addition, you also know that the first player always won in the end. Now your goal is to reconstruct the way T games turned out, if you know the following details: (1) The games have been played using normal table tennis rules, but with a key difference. The set always ends when a player reaches 11 points (even when the score is 11-10, so no tiebreaks exist). (2) The match is played using a best of 5 system (the first player to win 3 sets wins the game). (3) The first player always won in the end...