NG0FRCTN - Fractions on Tree

题目描述

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: ### ![Fraction tree upto 3 levels](../../content/francky:CW "Fraction tree upto 3 levels") 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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

``````1
2
3
7
0``````

输出样例 #1

``````1/1
1/2
2/1
3/1``````