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: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
	static Scanner sc;
	static PrintWriter out;
	static char grid[][];
	static int h,w;
	static int memo[][];
	static final int uncal = -1,mod = 1_000_000_009;
	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		h = sc.nextInt();
		w = sc.nextInt();
		grid = new char[h][w];
		memo = new int[h][w];
		clear();
		for (int i = 0; i < h; i++) {
			grid[i] = sc.nextLine().toCharArray();
		}
		out.println(dp(0, 0));
		out.flush();
		out.close();
	}
	static void clear() {
		for(int[]a:memo){
			Arrays.fill(a, uncal);
		}
	}
	static int dp(int i,int j) {
		if(i+1 == h && j+1 == w) return 1;
		if(memo[i][j] != uncal)
			return memo[i][j];
		int right = 0,down =0;
		if(j+1<w && grid[i][j+1]=='.')
			right = dp(i, j+1)%mod;
		if(i+1<h && grid[i+1][j]=='.')
			down = dp(i+1, j)%mod;
		return memo[i][j] = (right + down)%mod;
	}
	static class Scanner{
		BufferedReader br;
		StringTokenizer st;
		public Scanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}
		private String next() throws Exception{
			while(st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws Exception{
			return Integer.parseInt(next());
		}
		public long nextLong() throws Exception{
			return Long.parseLong(next());
		}
		public double nextDouble() throws Exception{
			return Double.parseDouble(next());
		}
		public String nextLine() throws Exception {
			return br.readLine();
		}

	}
}