NMC 2016 Problem 3

Find all $a \in \mathbb{R}$ for which there exists a function $f: \mathbb{R} \rightarrow \mathbb{R}$, such that

(i) $f(f(x))=f(x)+x$, for all $x \in \mathbb{R}$,

(ii) $f(f(x)-x)=f(x)+$ ax, for all $x \in \mathbb{R}$.