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)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pair = System.Tuple<int, int>;
using Edge = System.Tuple<int, int, long>;
//using Debug;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var hw = Input.ar;
        var gred = Input.gred(hw[0]);
        var dp = new long[hw[0], hw[1]];
        var Hg = new[] { 0, 1, 0, -1 };
        var Wg = new[] { 1, 0, -1, 0 };
        var th = new bool[hw[0], hw[1]];
        var que = new Queue<Pair>();
        que.Enqueue(new Pair(0, 0));
        dp[0, 0] = 1;
        while (que.Count != 0)
        {
            var p = que.Dequeue();
            for(var i = 0; i < 4; i++)
            {
                var h = Hg[i] + p.Item1;
                var w = Wg[i] + p.Item2;
                if (!Search.IsInside(h, w, hw)) continue;
                if (!th[h, w] && i < 2 && gred[h][w] == '.')
                {
                    th[h, w] = true;
                    que.Enqueue(new Pair(h, w));
                }
                else if (i >= 2) dp[p.Item1, p.Item2] = (dp[p.Item1, p.Item2] + dp[h, w]) % Input.MOD;
            }
        }
        WriteLine(dp[hw[0] - 1, hw[1] - 1]);
    } 
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static string[] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read).ToArray();
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public const long Inf = (long)1e18;
    public const double eps = 1e-11;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class Search
{
    public static int UpperBound<T>(T[] array,T value)
        where T:IComparable<T>
    {
        var low = 0;
        var high = array.Length;
        while (high > low)
        {
            var mid = (high + low) / 2;
            if (array[mid].CompareTo(value) == 1) high = mid;
            else low = mid + 1;
        }
        return low;
    }

    public static int LowerBound<T>(T[] array,T value)
        where T : IComparable<T>
    {
        var low = 0;
        var high = array.Length;
        while (high > low)
        {
            var mid = (high + low) / 2;
            if (array[mid].CompareTo(value) != -1) high = mid;
            else low = mid + 1;
        }
        return low;
    }

    public static T Max<T>(params T[] array)
        => array.Max();
    public static T Min<T>(params T[] array)
        => array.Min();
    public static bool IsInside(int h, int w, int[] hw)
        => 0 <= h && h < hw[0] && 0 <= w && w < hw[1];
    public static bool IsPrime(long num)
    {
        if (num % 2 == 0 || num == 1) return false;
        for (var i = 3; i * i <= num; i += 2)
            if (num % i == 0) return false;
        return true;
    }
}