Let $P=\{x_1,x_2,\dots,x_L\}$ be an arithmetic progression in $\mathbb{Z}_N$ such that $Ld<N$, where $d$ is the difference of AP. In other words, $x_i-x_{i-1} \equiv d \pmod N$ for $i=\overline{2,L}$. Prove that $P$ can be represented as a disjoint union of two arithmetic progressions in $\mathbb{Z} $.
Would be grateful for explanation how to prove it.