A9644 | 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: $a,b,c$ $(1<=a<=5; 1<=b<=10000; -10000<=c<=10000)$ .

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 $10^{9}$ .