# Problem I. 115. (November 2005)

**I. 115.** It is well-known that every rational number *x* can uniquely be represented as a finite continued fraction:

where *a*_{0} is an integer, and *a*_{1},...,*a*_{n} are positive integers, further *a*_{n}>1. The terms of the continued fraction are obtained by a simple greedy algorithm. Number *a*_{0} can only be the integer part of *x*. If *x* is an integer, then we are ready. Otherwise, if *x* is not an integer, we have , with , and now we have to find a representation only for *y*.

Write a program that converts ordinary fractions into their continued fraction form.

The program should read the ordinary fractions from the standard input (*i.e.* from the keyboard). Every line will contain a fraction of the form *a*/*b*, where *a* and *b* are integers with at most 4 digits. Your program should display the continued fraction representation of these numbers on the standard output (*i.e.* on the monitor), using parentheses as in the example. Your program should stop if the standard input can not be read (``end of file''), or the input is an empty line.

See the *example. *

The source code of your program (`i115.pas`, `i115.c`, ...) should be submitted.

(10 pont)

**Deadline expired on December 15, 2005.**

### Statistics:

18 students sent a solution. 10 points: Balambér Dávid, Czigler András, Kiss Dániel Miklós, Szoldatics András, Szolnoki Lénárd, Véges Márton, Vincze János. 9 points: Gyüre Balázs, Szentandrási István. 8 points: 4 students. 7 points: 1 student. 3 points: 1 student. 1 point: 1 student. 0 point: 2 students.

Problems in Information Technology of KöMaL, November 2005