More than Nim
A two-player game is played with two piles of stones, with sizes \(m,n\). On a player's turn, that player can remove any positive integer number of stones from one pile, or the same positive integer number of stones from each pile. A player loses when they are unable to take a stone. If \(1 \leq m,n \leq 30\), for how many of the \(30 \times 30 = 900\) starting positions does the first player have a winning strategy?