probability good q

There are 2 players in this game. The first player starts, and only positive integers can be written down on a piece of paper. If the numbers a,b have been written on the piece of paper any number written after those two cannot be of the form ax+by where x,y are integers. The first player that writes down 1 loses the game. Determine if either 1st player or second player has a winning strategy.

assume that x,y>0