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Maximum Sum Square SubMatrix


Problem Description

Given a 2D integer matrix A of size N x N find a B x B submatrix where B<= N and B>= 1, such that sum of all the elements in submatrix is maximum.



Problem Constraints

1 <= N <= 103.

1 <= B <= N

-102 <= A[i][j] <= 102.



Input Format

First arguement is an 2D integer matrix A.

Second argument is an integer B.



Output Format

Return a single integer denoting the maximum sum of submatrix of size B x B.



Example Input

Input 1:

 A = [
        [1, 1, 1, 1, 1]
        [2, 2, 2, 2, 2]
        [3, 8, 6, 7, 3]
        [4, 4, 4, 4, 4]
        [5, 5, 5, 5, 5]
     ]
 B = 3

Input 2:

 A = [
        [2, 2]
        [2, 2]
    ]
 B = 2



Example Output

Output 1:

 48

Output 2:

 8



Example Explanation

Explanation 1:

    Maximum sum 3 x 3 matrix is
    8 6 7
    4 4 4
    5 5 5
    Sum = 48

Explanation 2:

 Maximum sum 2 x 2 matrix is
  2 2
  2 2
  Sum = 8



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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