P0015. Format of the numbers P57666


Statement
 

pdf   zip

html

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 ≥ 0, 2 ≤ b ≤ 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 ≤ |b| ≤ 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).

Public test cases
  • Input

        54321  10   5
         4321  10   5
       654321  10   5
         9999  10  20
          125   2   8
          125   3   8
          125   4   8
          125   5   8
          125   6   8
          125   7   8
          125   8   8
          125   9   8
    536870912   2   1
    536870912   2  32
            0   2   1
            0  10   2
    

    Output

    54321
    #4321
    *****
    ################9999
    #1111101
    ###11122
    ####1331
    ####1000
    #####325
    #####236
    #####175
    #####148
    *
    ##100000000000000000000000000000
    0
    #0
    
  • Information
    Author
    Professorat de P1
    Language
    English
    Translator
    Carlos Molina
    Original language
    Catalan
    Other languages
    Catalan
    Official solutions
    C++
    User solutions
    C++