 | help needed..
The Problem
A clever cat walks into a messy room which he needs to clean. Instead
of doing the work alone, it decides to have its helper cats do the
work. It keeps its (smaller) helper cats inside its hat. Each helper
cat also has helper cats in its own hat, and so on. Eventually, the
cats reach a smallest size. These smallest cats have no additional cats
in their hats. These unfortunate smallest cats have to do the cleaning.
The number of cats inside each (non-smallest) cat's hat is a constant,
N. The height of these cats-in-a-hat is 1/(N+1) times the height of the
cat whose hat they are in.
The smallest cats are of height one;
these are the cats that get the work done.
All heights are positive integers.
Given the height of the initial cat and the number of worker cats (of
height one), find the number of cats that are not doing any work (cats
of height greater than one) and also determine the sum of all the cats'
heights (the height of a stack of all cats standing one on top of
another).
The Input
The input consists of a sequence of cat-in-hat specifications. Each
specification is a single line consisting of two positive integers,
separated by white space. The first integer is the height of the
initial cat, and the second integer is the number of worker cats.
A pair of 0's on a line indicates the end of input.
The Output
For each input line (cat-in-hat specification), print the number of
cats that are not working, followed by a space, followed by the height
of the stack of cats. There should be one output line for each input
line other than the ``0 0'' that terminates input.
Sample Input
216 125
5764801 1679616
0 0
Sample Output
31 671
335923 30275911
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