MTS

A prisoner is planning to escape from prison. The prison’s gate consists of horizontal and vertical bars that are spaced one unit apart, so the area of each hole between the bars is 1x1. The prisoner manages to remove certain bars to make some bigger holes. Determine the area of the largest hole in the gate after the bars are removed.

Example
N = 6 (the number of horizontal bars initially)
M = 6 (the number of vertical bars initially)
H = [4] (an array of integers, the horizontal bars to remove)
V = [2] (an array of integers, the vertical bars to remove)

The first image depicts the initial prison gate with n = 6 horizontal and m = 6 vertical bars. The area of the biggest hole in the bars is 1x1. The second image depicts the same gate after the prisoner removes horizontal bar 4 and vertical bar 2, at which point the area of the biggest hole in the bars becomes 2x2 = 4

Sample input 1:
N = 3
M = 3
H = [2]
V = [2]
Output: 4

Sample input 2:
N = 2
M = 2
H = [1]
V = [2]
Output: 4

Sample input 3: 
N = 3
M = 2
H = [1,2,3]
V = [1,2]
Output:?

Given the input, return the area of the biggest hole in the prison gate’s bars.

Low-level design of a parking lot system.

This was an HM round, where along with the behavioural skills, I was asked HLD of MMT.