Counting - Addition and the Multiplication Counting Principle

SOURCE:COMPETITION
Number of Problems: 3. : (Book)

A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the 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?

$mathrm{(A) } 36 qquad mathrm{(B) } 37 qquad mathrm{(C) } 38 qquad mathrm{(D) } 39 qquad mathrm{(E) } 40$