Determining maximum possible number of pieces of a bar with given number of cuts I came across a challenge on Hackerrank which has me stumped literally. It is a coding problem but I am not looking for the code, rather I can't figure out the mathematical approach towards it. 

Problem Statement
Alex is attending a Halloween party with his girlfriend, Silvia. At
  the party, Silvia spots the corner of an infinite chocolate bar.
If the chocolate can be served as only 1 x 1 sized pieces and Alex can
  cut the chocolate bar exactly K times, what is the maximum number of
  chocolate pieces Alex can cut and give Silvia?
Input Format  The first line contains an integer T, the number of test
  cases. T lines follow. Each line contains an integer K.
Output Format T lines; each line should contain an integer that
  denotes the maximum number of pieces that can be obtained for each
  test case.
Constraints 1≤T≤10 2≤K≤107
Note: Chocolate must be served in 1 x 1 sized pieces. Alex can't
  relocate any of the pieces, nor can he place any piece on top of
  another.
Sample Input #00
4 5 6 7 8
Sample Output #00
6 9 12 16

Some places which aren't quite clear to me are: 


*

*What does the question mean by ... only 1 x 1 sized pieces? 

*How would you begin cutting an infinite chocolate bar?


I'd highly appreciate if someone could point out the mathematical logic behind this problem.

From the test cases, I am "deducing" that you are only allowed to cut infinite horizontal and vertical lines on the chocolate bar.... For instance two horizontal lines at heights 1 and 2 and three vertical ones at lengths 1,2,3 will leave 6 pieces drop...
Therefore, with m+n lines (horiz-vert) you get mn pieces. The problem now is maximize mn for a given m+n.
The answer should be easy, when m+n=2k, we get k^2, when m+n=2k+1, we get k(k+1)...
