DK-GEORGMOHR 2008 Problem 3

The numbers from $1$ to $500$ are written on the board. Two players $A$ and $B$ erase alternately one number at a time, and $A$ deletes the first number. If the sum of the last two number on the board is divisible by $3$ , $B$ wins, otherwise $A$ wins. Which player can lay out a strategy that ensures this player's victory?