Question 1

You have been assigned to design the flooring plan of an apartment. The apartment floor is a rectangle of length A and breadth B. You are allowed to place a tiles of integral lengths and breadths. You can not place a tile outside the apartment floor. In order to place tiles conveniently, it is necessary that all tiles share at least one side with any edge of the apartment floor.

The cost of each tile is said to be the square of the difference between the area of the tile and a fixed standard area K.

Task

Determine the minimum cost of flooring the apartment

Constraints