Problem:
Score : 100 points

Problem Statement

There is a grid with H horizontal rows and W vertical columns.
Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.

For each i and j (1 \leq i \leq H, 1 \leq j \leq W), Square (i, j) is described by a character a_{i, j}.
If a_{i, j} is ., Square (i, j) is an empty square; if a_{i, j} is #, Square (i, j) is a wall square.
It is guaranteed that Squares (1, 1) and (H, W) are empty squares.

Taro will start from Square (1, 1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.

Find the number of Taro's paths from Square (1, 1) to (H, W).
As the answer can be extremely large, find the count modulo 10^9 + 7.

Constraints

H and W are integers.

2 \leq H, W \leq 1000

a_{i, j} is . or #.

Squares (1, 1) and (H, W) are empty squares.

Input

Input is given from Standard Input in the following format:

H W
a_{1, 1}\ldotsa_{1, W}
:
a_{H, 1}\ldotsa_{H, W}

Output

Print the number of Taro's paths from Square (1, 1) to (H, W), modulo 10^9 + 7.

Sample Input 1

3 4
...#
.#..
....

Sample Output 1

3

There are three paths as follows:

Sample Input 2

5 2
..
#.
..
.#
..

Sample Output 2

0

There may be no paths.

Sample Input 3

5 5
..#..
.....
#...#
.....
..#..

Sample Output 3

24

Sample Input 4

20 20
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

Sample Output 4

345263555

Be sure to print the count modulo 10^9 + 7.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

#pragma warning disable

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Numerics;
using System.Collections;

static class MainClass
{
    public static void Main(string[] args)
    {
        var HW = Console.ReadLine().SplittedStringToInt32List();
        var H = HW[0];
        var W = HW[1];

        var grid = new bool?[H + 1,W + 1];
        for (int i = 0; i < H; i++)
        {
            var count = 0;
            Console.ReadLine().ToList().ForEach(x => grid[i, count++] = x == '#');
        }
        var ansgrid = new long[H + 1, W + 1];
        for (int i = 0; i < H+1; i++)
        {
            for (int j = 0; j < W+1; j++)
            {
                ansgrid[i, j] = 0;
            }
        }
        ansgrid[0, 0] = 1;
        var dx = new int[] { 1, 0 };
        var dy = new int[] { 0, 1 };
        var queue = new Queue<KeyValuePair<int, int>>();
        queue.Enqueue(new KeyValuePair<int, int>(0, 0));
        while (queue.Count != 0)
        {
            var item = queue.Dequeue();
            var num = 0l;
            if (item.Key - 1 >= 0)
                num += ansgrid[item.Key - 1, item.Value];
            if (item.Value - 1 >= 0)
                num += ansgrid[item.Key, item.Value - 1];
            if (item.Key == item.Value && item.Key == 0)
                num = 1;
            ansgrid[item.Key, item.Value] = num % 1000000007;
            for (int i = 0; i < 2; i++)
            {
                var x = item.Key + dx[i];
                var y = item.Value + dy[i];
                if (x < 0 || y < 0 || x >= H || y >= W)
                    continue;
                if (grid[x, y] == false)
                {
                    if (ansgrid[x,y] == 0)
                    {
                        queue.Enqueue(new KeyValuePair<int, int>(x, y));
                        grid[x, y] = null;
                    }
                }
            }
            if (ansgrid[H - 1, W - 1] != 0)
                break;
        }
        Console.WriteLine(ansgrid[H-1,W-1]);

        Console.ReadLine();
    }

    public static void PrintArray(int[,] array)
    {
        for (int i = 0; i < array.GetLength(0); i++)
        {
            for (int j = 0; j < array.GetLength(1); j++)
            {
                Console.Write(array[i, j] + " ");
            }
            Console.WriteLine();
        }
    }

    #region ライブラリ
    public static long ToInt64(this string str) => long.Parse(str);
    public static int ToInt32(this string str) => int.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static List<string> SplittedStringToList(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).ToList();
    public static List<int> SplittedStringToInt32List(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => int.Parse(x)).ToList();
    public static List<BigInteger> SplittedStringToBigInteger(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => BigInteger.Parse(x)).ToList();
    public const int INF = int.MaxValue / 2;
    public const long LONGINF = long.MaxValue / 2;
    #endregion
}