Maximum Path Score in a Grid

Description

You are given an m x n grid where each cell contains one of the values 0, 1, or 2. You are also given an integer k.

You start from the top-left corner (0, 0) and want to reach the bottom-right corner (m - 1, n - 1) by moving only right or down.

Each cell contributes a specific score and incurs an associated cost, according to their cell values:

- 0: adds 0 to your score and costs 0.

- 1: adds 1 to your score and costs 1.

- 2: adds 2 to your score and costs 1. ​​​​​​​

Return the maximum score achievable without exceeding a total cost of k, or -1 if no valid path exists.

Note: If you reach the last cell but the total cost exceeds k, the path is invalid.