CF460B 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 $ 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.

The first line contains three space-separated integers: $ a,b,c $ $ (1

Print integer $ n $ — the number of the solutions that you've found. Next print $ n $ integers in the increasing order — the solutions of the given equation. Print only integer solutions that are larger than zero and strictly less than $ 10^{9} $ .