CUBE  HYPERCUBES
Bhavik and Anurag are best and special friends,special in the sense that they both share their birthday's i.e June 6. Ironically,neither of them gives each or other friends birthday party owing to that fact.
Abhishek(aka "guttss") being a clever friend of both wants to have a party from either of them so he decided to present a problem on 'hypercubes'.(Abhishek loves maths as you know!).They cannot ignore what "Guttss" has to say hence they need to solve the problem or give him a party!!
Here is the problem:
A cube is an object that measures the same distance across in three perpendicular directions in a threedimensional space.
A fourdimensional hypercube is an object that measures the same distance across in four perpendicular directions in a 4d space.
Given dimension i , create a hypercubic array using 1x1x....x1(i times) hypercubes to form a big hypercube of side n.
Problem is to find the total number of 1x1x1...x1(i times) hypercubes on the surface of big hypercube.
Bhavik being his lazy self wants to sleep as well as solve this problem before Anurag does as who first solves the problem avoids giving bitrthday treat to "Guttss".
Help Bhavik solve the problem so that he can sleep peacefully by avoiding a treat:))
Input
t=no of testcases(<2000)
next t lines: two integers n and i.(3<=n,i<=100)
Output
For each testcase print in newline the required answer.
Example
Input: 1
3 3 Output: 26
Explanation: Take a rubik's cube(3x3x3 cubic array of 1x1x1 cubes) and count.:)
Note: A cube is a hypercube in 3D.
Hypercubic arrays are made using 1x1x...x1(i dimensions) hypercubes.
Warning:Time limit allows slower languages(java/python) to pass easily.However for faster languages(C/C++) answer might not fit in 64bit.
hide comments
David:
20210226 04:53:11
@lilpeep  The requirement of the problem is that the 1x hypercubes are on the surface of big hypercube. In 3 dimensions of a 3x3x3 cube, the center cube is not on the surface. Therefore, 3*3*31 = 26. 

lilpeep:
20200328 15:19:21
I counted rubiks cube 3x3x3 and it was not 26 ! :V help.


edyduk1234567:
20190703 06:59:06
blyt


nadstratosfer:
20171115 02:22:32
mahilewets, for us mortals with 3dimensional imagination it is a difficult problem. Deriving a formula is easy once presented with some results, but to get there one needs to do some research or be familiar with multidimensional geometry. 

mahilewets:
20170910 20:54:35
Implementation difficulty 23 percent???


candide:
20170410 22:04:11
Simple formula. Poor description, poor example, poor writing. Context character (Bhavik, etc) is just noise. Hypercube description is irrelevant (what difference with a hypersphere?). Hypercube term remains undefined, the same for the hypercube "surface". For a better understanding, try online SPOJ toolkit. Last edit: 20170411 09:35:59 

Siddharth Singh:
20160208 07:20:36
Too Easy in Python (PyPy 2.6) 

Vamsi Krishna Avula:
20141214 07:27:16
uff!, atlast AC in C++ 

wisfaq:
20140608 13:48:36
Last edit: 20140608 15:13:03 

Tanmay:
20140607 09:16:31
Can someone post answer for some test cases? Say, 4 5?

Added by:  Bhavik 
Date:  20140605 
Time limit:  0.5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Cube trilogy films 