Let $P(x)\in \mathbb Z[x]$ be an irreducible polynomial. Prove or disprove that $P\circ P$ is irreducible over $\mathbb Z$

Question

Let $P(x)\in \mathbb Z[x]$ be an irreducible polynomial. Prove or disprove that $P\circ P$ is irreducible over $\mathbb Z$.

---

I tried expanding $P(x)=\sum a_ix_i$ and then putting $P(P(k))=0$ assuming that $\nexists$ $r \ni P(r)=0 \forall r\in\mathbb{Z}$. I observed that $P(k)\mid \{\text{co-ef of }x^0\}$. And there's no more progress.

I think that it's not reducible but I cannot prove it.