Crazy numbers

Given three natural numbers $b$ , $d$ and $n$ , let us say that a natural number $x$ is crazy if $x$ is a multiple of $n$ , and $x$ represented in base $b$

has exactly $d$ digits (maybe with a leading zero),
and does not have two equal consecutive digits.

Given $b$ , $d$ and $n$ , can you find all crazy numbers?

Input

Input consists of several cases, each one with $b$ , $d$ and $n$ . You can assume $3 \le b \le 10$ , $d \ge 1$ , and $n < b^d \le 10^{17}$ .

Output

For every case, print in order and with exactly $d$ digits all crazy numbers in base $b$ , followed by a line with ten dashes. All given cases are such that there are between 1 and 100 crazy numbers.

Observation

The expected solution requires less than 0.1 seconds to solve Sample input 2.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T10:35:02.904Z