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B. Little Dima and Equation

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle 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:

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.

Input

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

Output

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}.

Examples

Input

3 2 8

Output

3

10 2008 13726

Input

1 2 -18

Output

0

Input

2 2 -1

Output

4

1 31 337 967

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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