A and B are going to play a game: two pots are filled with stones, one with 57 stones and the other with 62 stones.
A legal move consists of emptying a pot - throwing away all the stones it contains - and splitting the stones of the other pot among the two pots, so that each pot contains at least one stone.
Players A and B alternate their moves, and player A is the first to make a move.
If a player is unable to make a legal move, then he loses.
Who wins this game and what is his optimal play strategy?