Maximum Sum Submatrix

You are given a two-dimensional matrix of integers. Your task is to find the maximum sum of any non-empty contiguous submatrix. A submatrix is defined as a contiguous rectangular block of elements in the matrix. In mathematical terms, if the submatrix covers rows from r₁ to r₂ and columns from c₁ to c₂, then its sum is:

\[ S = \sum_{i=r_1}^{r_2} \sum_{j=c_1}^{c_2} a_{ij} \]

Your solution should efficiently handle matrices that might include negative numbers.

inputFormat

The first line of the input contains an integer T representing the number of test cases. Each test case begins with a line containing two integers N and M (the number of rows and columns, respectively). This is followed by N lines, each containing M space-separated integers representing the matrix.

For example:

1
4 5
1 2 -1 -4 -20
-8 -3 4 2 1
3 8 10 1 3
-4 -1 1 7 -6

outputFormat

For every test case, output a single line containing the maximum sum of any submatrix in the given matrix.

## sample

1
4 5
1 2 -1 -4 -20
-8 -3 4 2 1
3 8 10 1 3
-4 -1 1 7 -6

29

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