For any positive integer , denote the sum of digits of in its decimal representation by . Find all polynomials with integer coefficients such that for any positive integer , the integer is positive and
For any positive integer $k$, denote the sum of digits of $k$ in its decimal representation by $S(k)$. Find all polynomials $P(x)$ with integer coefficients such that for any positive integer $n \geq 2016$, the integer $P(n)$ is positive and $$S(P(n)) = P(S(n)).$$
Školjka 
, denote the sum of digits of 
. Find all polynomials 
with integer coefficients such that for any positive integer 
, the integer 
is positive and 