CR-MO 2003 Problem 1

Two players $A$ and $B$ participate in the following game. Initially we have a pile of 2003 stones. $A$ plays first, and he picks a divisor of 2003 and removes that number of stones from the pile. Then $B$ picks a divisor of the number of remaining stones, and removes that number of stones from the pile, and so forth. The players who removes the last stone loses. Prove that one of the players has a winning strategy and describe it.