P0015. Format of the numbers P57666

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).