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.*;
public class Main{
   

  public static long ways(char matrix[][],int n,int m,int i,int j,long dp[][])
  {
	  
	  if(matrix[i][j]=='#') {
		  dp[i][j]=0;
		  return 0;}
	  if(i==n-1&&j==m-1)
		  return 1;
	  if(dp[i][j]==-1) {
	  int dx=i+1;
	  int dy=j;
	  int rx=i;
	  int ry=j+1;
	  long op1=0,op2=0;
	  if(dx<n&&dy<m)
	  {
		if(dp[dx][dy]==-1)
			op1=(ways(matrix,n,m,dx,dy,dp))%1000000007;
		else
			op1=dp[dx][dy];
	  }
	  if(rx<n&&ry<m)
	  {
		if(dp[rx][ry]==-1)
			op2=ways(matrix,n,m,rx,ry,dp)%1000000007;
		else
			op2=dp[rx][ry];
	  }
	  dp[i][j]=(op1+op2)%1000000007;
	  
	  
	  }
	  return dp[i][j];
  }
	
  public static void main(String[] args)
  {
     
  Scanner s=new Scanner(System.in);
  int n=s.nextInt();
  int m=s.nextInt();
  char matrix[][]=new char[n][m];
  for(int i=0;i<n;i++)
  {
	String line=s.next();
	String str[]=line.split("");
	  for(int j=0;j<m;j++) {
		  matrix[i][j]=str[j].charAt(0);}
  }
  long dp[][]=new long[n][m];
  for(int i=0;i<n;i++)
  {
	  for(int j=0;j<m;j++)
	  {
		  dp[i][j]=-1;
	  }
  }
//  for(int p=0;p<n;p++)
//  {
//	  for(int q=0;q<m;q++)
//		 System.out.print(matrix[p][q]+" ");
//	  System.out.println();
//  }
// 
  System.out.println( ways(matrix,n,m,0,0,dp));
  
  s.close();
    
  }
}