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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.io.*;

public class Main{
	static long[][]memo;
	static char[][] map;
	public static void main(String[] args) throws NumberFormatException, IOException, InterruptedException {
		// System.out.println("adfsf");
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int h=sc.nextInt();
		int w=sc.nextInt();
		map=new char[h][w];
		for (int i = 0; i < h; i++) {
			String s=sc.next();
			for (int j = 0; j < w; j++) {
				map[i][j]=s.charAt(j);
			}
		}
		//System.out.println(Arrays.deepToString(map));
		memo=new long[h][w];
		for (long[] x : memo) {
			Arrays.fill(x, -1);
		}
		memo[h-1][w-1]=1;
		System.out.println(dp(0,0));
	}
	static long dp(int h,int w) {
		if(memo[h][w]!=-1)
			return memo[h][w]=(long)(memo[h][w]%(1e9+7));
		if(map[h][w]=='#')
			return memo[h][w]=0;
		long x=0;
		if(valid(h+1,w))
			x+=dp(h+1,w);
		if(valid(h,w+1))
			x+=dp(h,w+1);
		return memo[h][w]=x%=(1e9+7);
		
	}
	private static boolean valid(int h, int i) {
		return h<map.length&&i<map[0].length;
	}
	static void shuffleArray(int[] ar) {
		// If running on Java 6 or older, use `new Random()` on RHS here
		Random rnd = ThreadLocalRandom.current();
		for (int i = ar.length - 1; i > 0; i--) {
			int index = rnd.nextInt(i + 1);
			// Simple swap
			int a = ar[index];
			ar[index] = ar[i];
			ar[i] = a;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}

}