There are two piles of balls. One contains $5$ balls and the other contains $18$ balls.
$A$ and $B$ are playing the following game: In each round, a player has to move balls from the larger pile to the smaller pile such that the number moved was a non-zero multiple of how many were previously in the smaller pile. $A$ starts, and $A$ and $B$ alternate until a pile of balls is empty. The person who emptied it is the winner.
Who will win this game?