SP5640 NG0FRCTN - Fractions on Tree

A fraction tree is an infinite binary tree defined as follows: 1\) Every node of tree contains a fraction 2\) Root of tree contains the fraction 1/1 3\) Any node with fraction i/j has two children : left child with fraction i/(i+j) and right child with fraction (i+j)/j For example , fraction tree upto 3 levels is as shown: ###  We number the nodes according to increasing levels ( root is at level 1) and at any same level , nodes are numbered from left to right. So first node holds the fraction 1/1 , second one holds 1/2 , third one holds 2/1 fourth one holds 1/3 and so on. Your task is simple. Given a number n , you are to find the fraction at the nth node.

Every line of the input contains a single number n. You are to find the fraction at nth node of fraction tree. Input file terminates with a 0 which is not to be processed.

For each input , print numerator and denominator of the lowest form of the fraction seperated by a /. Output of each case to be done in seperate lines.