US-TST 2003 Problem 1

For a pair of integers $a$ and $b$ , with $0 < a < b < 1000$ , set $S\subseteq \{ 1, 2, \dots , 2003\}$ is called a skipping set for $(a, b)$ if for any pair of elements $s_1, s_2 \in S$ , $|s_1 - s_2|\not\in \{ a, b\}$ . Let $f(a, b)$ be the maximum size of a skipping set for $(a, b)$ . Determine the maximum and minimum values of $f$ .