Little Dima and Equation

题意翻译

给定一个函数 $S(x)$ 表示 $x$ 的十进制表示下的数码和（例如 $123$ 的数码和就是把三个数加起来为 $6$）,给定常数 $a$,$b$,$c$。其中给定等式 $$x=b*S(x)^a+c $$ 当 $x$ 严格小于 $10^9$ 且满足此等式时，则 $x$ 是所求答案之一。最后输出所有存在的 $x$ 的数量和值。

题目描述

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.

输入输出格式

输入格式

The first line contains three space-separated integers: $ a,b,c $ $ (1<=a<=5; 1<=b<=10000; -10000<=c<=10000) $ .

输出格式

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} $ .

输入输出样例

输入样例 #1

3 2 8

输出样例 #1

3
10 2008 13726 

输入样例 #2

1 2 -18

输出样例 #2

0

输入样例 #3

2 2 -1

输出样例 #3

4
1 31 337 967