Splitting $\mathbb Z_{pq}$ into direct sum with $\mathbb Z_p$

Question

I'm trying to show there exists $T \subseteq \mathbb Z_{pq}$ such that $\mathbb Z_{pq} = \mathbb Z_p \oplus T$, where $p$ and $q$ are distinct primes.

I tried to use Chinese Remainder so we know $\mathbb Z_{pq} = \mathbb Z_p \times \mathbb Z_q$. Not sure what to do next.