Problems
Continued Fractions
Continued Fractions
Let b0
, b1
, b2
, ..., bn
be integers with bk
> 0 for k > 0. The continued fraction of order n with coefficients b1
, b2
, ..., bn
and the initial term b0
is defined by the following expression
which can be abbreviated as [b0
; b1
, ..., bn
].
An example of a continued fraction of order n = 3 is [2;3,1,4]. This is equivalent to
Write a program that determines the expansion of a given rational number as a continued fraction. To ensure uniqueness, make bn
> 1.
Input
Consists of an undetermined number of rational numbers. Each rational number is defined by two integers, numerator and denominator.
Output
For each rational number output the corresponding continued fraction on a separate line.
Input example #1
43 19 1 2
Output example #1
[2;3,1,4] [0;2]