CR-MO 2010 Problem 6

Let $F$ be the family of all sets of positive integers with $2010$ elements that satisfy the following condition: The difference between any two of its elements is never the same as the difference of any other two of its elements. Let $f$ be a function defined from $F$ to the positive integers such that $f(K)$ is the biggest element of $K \in F$ . Determine the least value of $f(K)$ .