from typing import List
"""
Multiplies two matrices M and N and returns the resulting matrix.
Args:
    M (List[List]): The first matrix as a list of lists, with dimensions m x k.
    N (List[List]): The second matrix as a list of lists, with dimensions k x n.
Returns:
    List[List]: The product matrix as a list of lists, with dimensions m x n.
Raises:
    AssertionError: If the number of columns in M does not equal the number of rows in N.
Example:
    >>> M = [
    ...     [1, 2, 4],
    ...     [0, 1, 2]
    ... ]
    >>> N = [
    ...     [1, 2],
    ...     [3, 4],
    ...     [0, 1]
    ... ]
    >>> multiply(M, N)
    [[7, 14], [3, 6]]
    
NOTE: If you import the matrix_mult module into another project, call it with matrix_mult.multiply(M, N).

"""


def multiply(M: List[List], N: List[List]) -> List[List]:
    mrows, mcols = len(M), len(M[0])
    nrows, ncols = len(N), len(N[0])
    assert mcols == nrows, "Matrices are not compatible for multiplication"
    # Initialize result matrix with zeros
    result = [[0 for _ in range(ncols)] for _ in range(mrows)]
    for i in range(mrows):
        for j in range(ncols):
            for k in range(mcols):
                result[i][j] += M[i][k] * N[k][j]
    return result