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
dr_br34k:
20170627 14:58:37
Think of O(1) solution every ith new slant line is made of i elements.


anilkumar1998:
20170609 19:44:47
Try to think of O(1) solution. 

codervrinda:
20170529 07:09:27
nice problem:) !


viratian_070:
20170527 12:55:22
AC in one go!! took some time in finding the formula though!!


ramesh_961:
20170526 07:25:31
AC in One Go!!Easy if you carefully observe the sequence!! 

akhil9093:
20170328 19:02:52
AC in one go..yipeee!!!! 

caohoangtung:
20170325 15:51:40
AC in 1 go :) Nice problem 

vladimira:
20170218 14:40:44
Hello everyone. I've written script in python 3. 13 lines of code: one range loop, one sqrt use, one ceil, some ariphmetic and one print. Why my solution uses 30 MB when all other people < 10MB? Last edit: 20170218 14:48:18 

nilabja16180:
20170209 21:57:48
AC in one Go, Triangular Number is the key!! 

arindam1234:
20170121 19:03:03
AC!!! My 100th on spoj. 
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 