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.*;
public class Main {
  public static void main(String[] args) throws IOException,InterruptedException{
	Scanner sc =new Scanner(System.in);
	PrintWriter pw = new PrintWriter(System.out);
	int n =sc.nextInt(),m=sc.nextInt();
	char [][] arr=new char[n][m];
	for (int i=0;i<n;++i)
		arr[i]=sc.next().toCharArray();
	long mod =(int)1e9+7;
	long [] [] poss=new long [n][m];
	poss[0][0]=1;
	for (int i =0;i<n;++i)
		for (int j=0;j<m;++j) {
			if (arr[i][j]=='#')
				continue;
			poss[i][j]+=((i-1>=0&&arr[i-1][j]=='.')?poss[i-1][j]:0)%mod;
			poss[i][j]+=((j-1>=0&&arr[i][j-1]=='.')?poss[i][j-1]:0)%mod;
		}
	//System.out.println(Arrays.deepToString(poss));
	pw.println(poss[n-1][m-1]%mod);
	pw.flush();
  }
  static long gcd (long a ,long b)
  {
	  return (b==0)?a:gcd(b, a%b);
  }
  static long [] gcd2 (long a ,long b) {
	  if (b==0)
		  return new long [] {a,1,0};
	  long [] val =gcd2(b, a%b);
	  long gcd =val[0];
	  long x =val[2],y=val[1]-(a/b)*val[2];
	  return new long [] {gcd,x,y};
  }
  static class Scanner {
		StringTokenizer stringTokenizer;	
		BufferedReader bfBufferedReader;
		public Scanner(InputStream system) {
			bfBufferedReader=new BufferedReader(new InputStreamReader( system));
		}
		 public Scanner(String file) throws Exception {
	            bfBufferedReader = new BufferedReader(new FileReader( file));
	        }			 
	        public String next() throws IOException {
	            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens())
	                stringTokenizer = new StringTokenizer( bfBufferedReader.readLine());
	            return stringTokenizer.nextToken();
	        }
	 
	        public String nextLine() throws IOException {
	            return bfBufferedReader.readLine();
	        }
	 
	        public int nextInt() throws IOException {
	            return Integer.parseInt(next());
	        }
	 
	        public double nextDouble() throws IOException {
	            return Double.parseDouble(next());
	        }
	 
	        public char nextChar() throws IOException {
	            return next().charAt(0);
	        }
	 
	        public Long nextLong() throws IOException {
	            return Long.parseLong(next());
	        }
	 
	        public boolean ready() throws IOException {
	            return bfBufferedReader.ready();
	        }
	 
	        public void waitForInput() throws InterruptedException {
	            Thread.sleep(3000);
	        }
  }
  }