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 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.

输入描述:

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

输出描述:

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.