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
dileep_32:
20210319 04:01:11
GIVEN TEST CASE IS CORRECT 

tejasreddyk:
20210116 17:25:49
HHAHA AC in one go


naveen1948:
20201108 08:19:10
check the output format carefully orelse you will be doomed


npoudel21:
20201004 06:06:59
Isn't the sample answer wrong? Shouldn't the 14th term be 4/2


saurabh_shinde:
20200910 15:57:29
easy in concept. just slight tricky to implement 

coolboy7:
20200604 18:26:11
Hint if you are not able to solve the problem:


manish_thakur:
20191212 12:28:09
position(x,y) = (1/2)(x+y)(x+y+1) + y


gak:
20191028 10:53:57
Observe the pattern by summing numerator and denominator, after that it's a cakewalk. 

saraswat000:
20190827 21:08:22
AC in one go! 

mriow:
20190820 09:02:27
Solution can be achieved in O(1) for every Cantor's Term.

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 