2001 OIM Problems/Problem 5

Problem

On a $2000 \times 2001$ board the squares have coordinates $(x, y)$ with $x, y$ integers, $0 \le x \le 1999$ and $0 \le y \le 2000$ . A ship on the board moves as follows: Before each movement, the ship is in a position $(x, y)$ and has a speed $(h, v)$ where $h$ and $v$ are integers. The ship chooses a new speed $(h',v')$ such that $h'-h$ be equal to $-1, 0$ or $1$ and $v'-v$ be equal to $-1, 0$ or $1$ . The new position of the ship will be $(x',y')$ where $x'$ is the reminder of the division of $x+h'$ by 2000, and $y'$ is the reminder of the division of $y+v'$ by 2001. There are two ships on the board: the Martian one and the Earth one that wants to catch the Martian one. Initially each ship is on a square on the board and has speed $(0, 0)$ . Earth ship moves first and continue moving alternately. Is there a strategy that always allows the Earth ship to catch the Martian ship, whatever the initial positions are?