CANTON  Count on Cantor
One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.
1/1 1/2 1/3 1/4 1/5 ... 2/1 2/2 2/3 2/4 3/1 3/2 3/3 4/1 4/2 5/1
In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.
Input
The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.
Then, it contains a single number per line.
Output
You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.
Example
Input: 3 3 14 7 Output: TERM 3 IS 2/1 TERM 14 IS 2/4 TERM 7 IS 1/4
hide comments
Tony T.:
20150401 05:04:12
Need to know a couple of equations on triangular numbers. The rest is just conceptualising how the terms move along the diagonal. 

NESTOR IGNACIO BERNAL MORALES:
20150305 22:29:57
Yeah 

Yash:
20150206 23:10:15
AC in 1st go :) My 75th on spoj :) 

Pratik:
20150129 06:58:45
How is third term not 1/3


Harsh Shah:
20150128 19:17:53
Learnt new technique, great question. 

:.Mohib.::
20150118 11:40:51
Easy...got It..... :) 

SM_92:
20150101 18:55:57
Last edit: 20150103 09:35:52 

Saksham :
20141224 19:49:53
ac in first go


kartikay singh:
20141211 07:13:32
AC in 0.0 sec yepieee 

kartikay singh:
20141211 07:12:41
silly mistakes cost me 2 WA but finally AC .........

Added by:  ThanhVy Hua 
Date:  20050227 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM South Eastern European Region 2004 