spoj#NG1FRCTN. Fractions on Tree ( reloaded !)

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:

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, 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.

 

Input

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.

 

Output

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.

Example

Input:
1 1
1 2
2 4
0 0

Output:
1/1
1/2
1/3

Constraints : 1<=T <=30000 1<=a<=b<=10^10
1
1
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2
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3
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1 
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