Unique Path in Grid

Given a grid of characters, where . represents an empty cell and # represents an obstacle, determine whether there exists exactly one unique valid path from the top-left corner to the bottom-right corner. From any cell, you are only allowed to move either right or down.

The path is considered valid if it does not go through any obstacles. If there is exactly one valid path, output YES; otherwise, output NO.

Note: Use dynamic programming to efficiently count the total number of paths to the destination.

inputFormat

The first line contains two integers n and m --- the number of rows and columns of the grid.

Each of the next n lines contains a string of m characters, where each character is either . (empty cell) or # (obstacle).

outputFormat

Output a single line: YES if there is exactly one valid path from the top-left to the bottom-right, or NO otherwise.

3 3
..#
.#.
...

YES