maximum-path-score-in-a-grid

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.

Example 1:

Input: grid = [[0, 1],[2, 0]], k = 1

Output: 2

Explanation:​​​​​​​

The optimal path is:

Thus, the maximum possible score is 2.

Example 2:

Input: grid = [[0, 1],[1, 2]], k = 1

Output: -1

Explanation:

There is no path that reaches cell (1, 1)​​​​​​​ without exceeding cost k. Thus, the answer is -1.

Constraints:

• 1 <= m, n <= 200


• 0 <= k <= 103​​​​​​​


• ​​​​​​​grid[0][0] == 0


• 0 <= grid[i][j] <= 2