AMC 12 2004a Problem 7

A game is played with tokens according to the following rules. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard pile. The game ends when some player runs out of tokens. Players $A$, $B$ and $C$ start with $15$, $14$ and $13$ tokens, respectively. How many rounds will there be in the game?

$\text{(A) } 36 \text{(B) } 37 \text{(C) } 38 \text{(D) } 39 \text{(E) } 40$