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All leaked interview problems are collected from Internet.

Given a non-empty 2D matrix *matrix* and an integer *k*, find the max sum of a rectangle in the *matrix* such that its sum is no larger than *k*.

**Example:**

Given matrix = [ [1, 0, 1], [0, -2, 3] ] k = 2

The answer is `2`

. Because the sum of rectangle `[[0, 1], [-2, 3]]`

is 2 and 2 is the max number no larger than k (k = 2).

**Note:**

- The rectangle inside the matrix must have an area > 0.
- What if the number of rows is much larger than the number of columns?

**Credits:**

Special thanks to @fujiaozhu for adding this problem and creating all test cases.

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