**Objective:** The goal of this assignment is to practice
recursion.

**Background.** Billions of people watch the Olympics, and
who knows, maybe the extraterrestrials are watching them too.
For them, the competitions are exciting, but the numerical
results may be difficult to understand: for us, with ten
fingers on both hands, it is natural to use a decimal system,
but creatures from other planets may use different bases. Let
us help them by designing a universal translator that, given a
positive integer n and a base B, prints the description of the
given number in the given base.

Examples:

- Creatures with three hands -- each of which
have 4 fingers -- can use 12-based system. In this system, a
decimal number 107 has the form 8 11, since 107 = 8 *
12
^{1}+ 11. - For a human-hand-like three-hand
creature with 3
* 5 = 15 fingers, the same number is represented as 107 = 7 2,
since 107 = 7 * 15
^{1}+ 2. - For a one-hand
creature with 6 fingers, 107 = 2 5 5, since 107 = 2 *
6
^{2}+ 5 * 6^{1}+ 5.

**Algorithm.** The algorithm for transforming the number
into base B is as follows:

- if the number n is smaller than the base B, then this same number is the desired representation;
- otherwise, if n ≥ B, we take the ratio n / B, convert it to base B (by using the same algorithm), and then append the remainder n % B at the end.

Example:

- Since 107 ≥ 6, we compute 107 / 6 = 17. When we transform 17 into base 6, we get 2 5 (see below). To get the desired representation of 107, we need to also print the remainder 107 % 6 = 5. The result will be the desired sequence 2 5 5.
- To convert 17, since 17 ≥ 6, we compute 17 / 6 = 2. When we convert this number into base 6, we get 2 (see below). To get the desired representation of 17, we need to also print the remainder 17 % 6 = 5. The result will be the sequence 2 5.
- To convert 2, since 2 < 6, we simply print 2.

**Testing.** Test your method on examples where it is easy
to manually compute the result: B = 10 and B = 2 (binary
code).