BALKAN-SL 2015 A6

For a polynomials $P\in \mathbb{R}[x]$ , denote $f(P)=n$ if $n$ is the smallest positive integer for which is valid $$(\forall x\in \mathbb{R})(\underbrace{P(P(\ldots P}_{n}(x))\ldots )>0),$$ and $f(P)=0$ if such n doeas not exist. Exists polyomial $P\in \mathbb{R}[x]$ of degree $2014^{2015}$ such that $f(P)=2015$ ?

(Serbia)