ÖMO 1997 Problem 2

A positive integer $K$ is given. Define the sequence $(a_n)$ by $a_1 = 1$ and $a_n$ is the $n$ -th positive integer greater than $a_{n-1}$ which is congruent to $n$ modulo $K$ .(a) Find an explicit formula for $a_n$ .(b) What is the result if $K = 2$ ?