MaxNiceMatrixDiv1

You are given three integers a, b, and c where a and b are non-negative and c is positive. A matrix X is said to be a nice (a,b,c)-matrix if the following conditions are met:

1. Every element of X is an integer between a and b, inclusive.
2. The matrix has exactly c columns.
3. In each column of X all the elements are distinct.
4. The sum of each row of X is equal to b+(c-1)*a.

Note that different nice (a,b,c)-matrices may have different numbers of rows. For instance, the following three matrices are nice (1,3,3)-matrices:

    matrix 1 (1 row, 3 columns):
        1 3 1

    matrix 2 (1 row, 3 columns):
        1 2 2

    matrix 3 (2 rows, 3 columns):
        2 2 1
        1 1 3

There are many other nice (1,3,3)-matrices. It can be shown that each nice (1,3,3)-matrix has either one or two rows.

You are given the three ints a, b, and c. Construct a nice (a,b,c)-matrix with as many rows as possible.

Suppose you constructed the matrix X with r rows and c columns. Return an array (a variable of type int[]) that contains all the elements of X in row-major order. In other words, return the following:

{
    X[0][0], X[0][1], ..., X[0][c-1],
    X[1][0], X[1][1], ..., X[1][c-1],
    ...,
    X[r-1][0], X[r-1][1], ..., X[r-1][c-1]
}

If there are multiple optimal matrices, you may return any of them.