INMO 1990 Problem 3

Let $f$ be a function defined on the set of non-negative integers and taking values in the same set. Given that

(a) $x - f(x) = 19\left[\frac{x}{19}\right] - 90\left[\frac{f(x)}{90}\right]$ for all non-negative integers $x$ ;

(b) $1900 < f(1990) < 2000$ ,

find the possible values that $f(1990)$ can take. (Notation : here $[z]$ refers to largest integer that is $\leq z$ , e.g. $[3.1415] = 3$ ).