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 < 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.

小迪马在数学课上屡次捣乱，严厉的皮克尔斯老师给了他如下题目作为惩罚。

找出方程的所有整数解 $x$（满足 $0 < x < 10^9$）：

$$x = b \cdot s(x)^a + c,$$

其中 $a$、$b$、$c$ 是预先给定的常数，函数 $s(x)$ 表示 $x$ 的十进制表示中所有数字之和。

老师每节课都给迪马布置这道题，仅更改方程的参数 $a$、$b$、$c$。迪马厌倦了因此得低分，于是请求你帮助他解决这个难题。

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

第一行包含三个用空格分隔的整数：$a$、$b$、$c$（$1 ≤ a ≤ 5$；$1 ≤ b ≤ 10000$；$-10000 ≤ c ≤ 10000$）。

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 109.

输出整数 $n$ —— 你所找到的解的个数。接下来按升序输出 $n$ 个整数 —— 给定方程的解。仅输出大于零且严格小于 $10^9$ 的整数解。