SDE - Intern

Ninja has been caged up in a prison and he is planning to escape from it. 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 (1 * 1). Ninja manages to remove certain bars and make some of these holes bigger. Your task is to determine the area of the largest hole in the gate after the bars are removed.

For example, let us consider that the initial prison gate with ‘n’ = 8 horizontal and ‘m’ = 8 vertical bars, where the area of the biggest hole in the bars is (1 * 1). If we remove the 4th horizontal bar and 6th vertical bar, then our maximum area will be (2 * 2).

You are given an array of integers 'arr' and an integer 'limit'.

Your task is to find the smallest positive integer divisor, such that upon dividing all the elements of the given array by it, the sum of the division's result is less than or equal to the given integer's limit.

Note:

Each result of the division is rounded to the nearest integer greater than or equal to that element. For Example, 7/3 = 3.