P0015. Format of the numbers

Given a natural $n$ , a basis $b$ and a natural number $c$ , we want to write $n$ in basis $b$ using exactly $c$ characters, following the next format:

If $n$ in basis $b$ has exactly $c$ digits, you only must write $n$ in basis $b$ .
If $n$ in basis $b$ has less than $c$ digits, you must add hashes on the left.
If $n$ in basis $b$ has more of $c$ digits, you must write $c$ asterisks instead of $n$ .

Your task is to write a program that, given a sequence of triplets $n$ , $b$ , $c$ , prints for each one a line following this format.

Input

The input is a sequence of triplets $n$ , $b$ , $c$ , with $n \ge 0$ , $2 \le b \le 10$ and $c > 0$ .

Output

For each triplet of the input, print a line according to the described format.

Observations

Strings are not allowed in this problem.
We suggest you to use a function @number_of_digits(n, b)@ that, given two natural numbers |n| and |b| with $2 \le |b| \le 10$ , returns the number of digits that requires the representation of |n| in basis |b|.
You must use recursion to write $n$ in basis $b$ (without the hashes).

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T11:28:11.747Z