CN-LEAGUE 2017 Problem 4

Let $m,n$ be integers greater than 1, $m \geq n$ , $a_1,a_2,\dots,a_n$ are $n$ distinct numbers not exceed $m$ ,which are relatively primitive.Show that for any real $x$ ,there exists $i$ for which $||a_ix|| \geq \frac{2}{m(m+1)} ||x||$ ,where $||x||$ denotes the distance between $x$ and the nearest integer to $x$ .