Given an m x n integer matrix grid, where each cell contains either $0$ (empty) or $1$ (obstacle), you may move one step at a time in any of the four directions (up, down, left, right), but only into empty cells.

Return the minimum number of steps required to travel from the upper-left corner $($0, 0$)$ to the lower-right corner $($m - 1, n - 1$)$, given that you are allowed to eliminate at most k obstacles along the way. If no such path exists, return $-1$.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \leq$ m, n $\leq 40$

• $1 \leq$ k $\leq$ m * n

• grid[i][j] is either $0$ or $1$

• grid[0][0] == grid[m - 1][n - 1] == 0

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.