Program | CAT.C,CAT.CPP,CAT.PAS |
(An homage to Theodore Seuss Geisel)
The Cat in the Hat is a nasty creature, With one flick of his wrist he pops his top off. Do you know what's inside that Cat's hat? Each little cat does the same as line three, Because the littlest cats have to clean all the grime, |
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; |
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 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.
216 125
5764801 1679616
0 0
31 671
335923 30275911