Codeforces Round #262(div2) B. Little Dima and Equation

Little Dima misbehaved during a math lesson a lot and the nasty teacher Mr. Pickles gave him the following problem as a punishment. Find all integer solutions x (0?? x ??10 9 ) of the equation: x ?=? b · s ( x ) a ?? c ,? where a , b , c

Little Dima misbehaved during a math lesson a lot and the nasty teacher Mr. Pickles gave him the following problem as a punishment.

Find all integer solutions x (0?x?109) of the equation:

x?=?b·s(x)a?+?c,?

where a, b, c are some predetermined constant values and function s(x) determines the sum of all digits in the decimal representation of number x.

The teacher gives this problem to Dima for each lesson. He changes only the parameters of the equation: a, b, c. Dima got sick of getting bad marks and he asks you to help him solve this challenging problem.