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 $a,b,c$。
给定等式 $x=b\times S(x)^a+c $,求出所有满足此等式且 $0 < x < 10 ^ 9$ 的 $x$。
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