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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.math.BigInteger;
public class Main {
	public static void main(String[] args) throws Exception {
		FastScanner sc = new FastScanner();
		PrintWriter pw = new PrintWriter(System.out);
		int l = sc.nextInt();
		int t = sc.nextInt();
		int[][] grid = new int[l][t];
		boolean[][] rocks = new boolean[l][t];
		for(int i=0;i<l;i++) {
			String str = sc.nextToken();
			for(int j=0;j<t;j++) {
				rocks[i][j]=str.charAt(j)=='.';
			}
		}
		int x=0;
		while(x<l&&rocks[x][0]) {
			grid[x++][0]=1;
		}
		x=0;
		while(x<t&&rocks[0][x]) {
			grid[0][x++]=1;
		}
		for(int i=1;i<l;i++) {
			for(int j=1;j<t;j++) {
				if(!rocks[i][j])grid[i][j]=0;
				grid[i][j]=(get(grid,i,j-1,rocks)+get(grid,i-1,j,rocks))%(int)(1e9+7);
			}
		}
		pw.println(grid[l-1][t-1]);
		pw.close();
	}
	static int get(int[][] arr, int x,int y, boolean[][] rocc) {
		if(x<0||y<0||x>=arr.length||y>=arr[0].length||!rocc[x][y])return 0;
		else return arr[x][y];
	}
}
@SuppressWarnings("all")
class FastScanner {
    BufferedReader br;
    StringTokenizer st;
 
    public FastScanner(String s) {
        try {
            br = new BufferedReader(new FileReader(s));
        } catch (FileNotFoundException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
    }
 
    public FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
 
    String nextToken() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt() {
        return Integer.parseInt(nextToken());
    }
 
    long nextLong() {
        return Long.parseLong(nextToken());
    }
 
    double nextDouble() {
        return Double.parseDouble(nextToken());
    }
}