Chinese Mathematical Olympiad

Given two integers $m,n$ greater than $1$, and integers $a_1<a_2<\cdots <a_m$, prove that there exists a set $T$ of integers with $|T|\le 1+\frac{a_m-a_1}{2n+1}$ such that each $a_i$ can be written as $a_i=t+s$ for some $t\in T$, and $s\in [-n,n]$. (Posed by Leng Gangsong)