CMO 2011 Problem 5

Let $d$ be a positive integer. Show that for every integer $S$, there exists an integer $n>0$ and a sequence $\epsilon_{1}, \epsilon_{2}, \ldots, \epsilon_{n}$, where for any $k, \epsilon_{k}=1$ or $\epsilon_{k}=-1$, such that

$$S=\epsilon_{1}(1+d)^{2}+\epsilon_{2}(1+2 d)^{2}+\epsilon_{3}(1+3 d)^{2}+\cdots+\epsilon_{n}(1+n d)^{2}$$