3565. Sequential Grid Path Cover

You are given a 2D array grid of size m x n, and an integer k. There are k cells in grid containing the values from 1 to k exactly once, and the rest of the cells have a value 0.

You can start at any cell, and move from a cell to its neighbors (up, down, left, or right). You must find a path in grid which:

• Visits each cell in grid exactly once.
• Visits the cells with values from 1 to k in order.

Return a 2D array result of size (m * n) x 2, where result[i] = [xi, yi] represents the ith cell visited in the path. If there are multiple such paths, you may return any one.

If no such path exists, return an empty array.

Example 1:

Example 2:

Constraints:

• 1 <= m == grid.length <= 5
• 1 <= n == grid[i].length <= 5
• 1 <= k <= m * n
• 0 <= grid[i][j] <= k
• grid contains all integers between 1 and k exactly once.