CMO 2013 Problem 6

Let $m,n$ be positive integers. Find the minimum positive integer $N$ which satisfies the following condition. If there exists a set $S$ of integers that contains a complete residue system module $m$ such that $| S | = N$ , then there exists a nonempty set $A \subseteq S$ so that $n\mid {\sum\limits_{x \in A} x }$ .