OMM 2003 Problem 5

Some cards each have a pair of numbers written on them. There is just one card for each pair $(a,b)$ with $1 \leq a < b \leq 2003$ . Two players play the following game. Each removes a card in turn and writes the product $ab$ of its numbers on the blackboard. The first player who causes the greatest common divisor of the numbers on the blackboard to fall to $1$ loses. Which player has a winning strategy?