RS-SMO 2013 Problem 1

Let $k$ be a natural number. Bijection $f:\mathbb{Z} \rightarrow \mathbb{Z}$ has the following property: for any integers $i$ and $j$ , $|i-j|\leq k$ implies $|f(i) - f(j)|\leq k$ . Prove that for every $i,j\in \mathbb{Z}$ it stands: $$|f(i)-f(j)|= |i-j|.$$