Problems

# Continued Fractions

# Continued Fractions

Let `b`

, _{0}`b`

, _{1}`b`

, ..., _{2}`b`

be integers with _{n}`b`

> _{k}**0** for **k** > **0**. The *continued fraction* of order **n** with coeficients `b`

, _{1}`b`

, ..., _{2}`b`

and the initial term _{n}`b`

is defined by the following expression_{0}

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**.

#### 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]