Create Grid With Exactly One Path

You are given two integers m and n, representing the number of rows and columns of a grid.

Construct any m x n grid consisting only of the characters '.' and '#', where:

A valid path is a sequence of free cells that:

Starts at the top-left cell (0, 0).
Ends at the bottom-right cell (m - 1, n - 1).
Moves only:
- Right, from (i, j) to (i, j + 1), or
- Down, from (i, j) to (i + 1, j).

Return any grid such that there is exactly one valid path from the top-left cell to the bottom-right cell.

Example 1:

Input: m = 2, n = 3

Output: ["..#","#.."]

Explanation:

The only valid path is: (0,0) → (0,1) → (1,1) → (1,2)

Example 2:

Input: m = 3, n = 3

Output: ["..#","#..","##."]

Explanation:

The only valid path is: (0,0) → (0,1) → (1,1) → (1,2) → (2,2)

Example 3:

Input: m = 1, n = 4

Output: ["...."]

Explanation:

The only valid path is: (0,0) → (0,1) → (0,2) → (0,3)

Constraints:

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