Taco Grid Paths

You are given an R×C grid where each cell is either open (denoted by .) or blocked (denoted by #). Starting from the top-left corner, your task is to determine the number of valid paths that lead to the bottom-right corner. In each step you can move either right or down. The answer should be computed modulo \(10^9+7\).

For example, consider the following test cases:

• For a 3×3 grid: ...\n.#.\n..., there are 2 valid paths.
• For a 1×1 grid with a single open cell (.), there is exactly 1 valid path.
• For a 3×3 grid: .#.\n###\n..., there is no valid path.
• For a 4×4 grid where all cells are open, there are 20 valid paths.

inputFormat

The input is read from standard input. The first line contains two integers R and C, representing the number of rows and columns. Each of the next R lines contains a string of length C consisting of characters '.' (open cell) and '#' (blocked cell).

outputFormat

Output a single integer on standard output which is the number of valid paths from the top-left corner to the bottom-right corner of the grid, computed modulo (10^9+7).## sample

3 3
...
.#.
...

2