SP5673 NG1FRCTN - Fractions on Tree ( reloaded !)

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, as always !. Given two numbers a and b , you are to find the product of fractions at all those nodes whose number is between a and b both inclusive.

Every line of the input contains two numbers a and b seperated by a space. You are to find the product of all fractions which are at node having number between a and b both inclusive. Input file terminates with a 0 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.