Let b[0]
, b[1]
, b[2]
, ..., b[n]
be integers with b[k]
> 0 for k > 0. The continued fraction of order n with coefficients b[1]
, b[2]
, ..., b[n]
and the initial term b[0]
is defined by the following expression
which can be abbreviated as [b[0]
; b[1]
, ..., b[n]
].
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 b[n]
> 1.
Consists of an undetermined number of rational numbers. Each rational number is defined by two integers, numerator and denominator.
For each rational number output the corresponding continued fraction on a separate line.