There are two rock piles. The first pile contains N rocks, and the second one contains M rocks, where
($0 ≤ N, M ≤ 10^{9}$) .
First and second players take turns to play the game, In each turn, a player can choose to take one rock from a single pile, or take one rock from both piles. The player who cannot make any move, loses the game.
So I don't know how to modify the xor equation to work with this case?
Hint: Losing positions are $(N,M)$ such that $N$ and $M$ are both even.