VN-TST 2014 Problem 5

Find all polynomials $P(x),Q(x)$ which have integer coefficients and satify the following condtion: For the sequence $(x_n )$ defined by $$x_0=2014,x_{2n+1}=P(x_{2n}),x_{2n}=Q(x_{2n-1}) n\geq 1$$ for every positive integer $m$ is a divisor of some non-zero element of $(x_n )$