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.io.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.io.BufferedReader; 
import java.util.*;

class Main{
	public static FastReader fs = new FastReader();
	static long mod = 1_000_000_00_7;
	static PrintWriter out = new PrintWriter(System.out);
	
	static void solve() {
		StringBuffer output = new StringBuffer();
		int h = fs.nextInt(),w = fs.nextInt();
		char g [][] = new char[h][w];
		for(int i = 0; i<h; i++) {
			g[i] = fs.next().toCharArray();
		}
		long dp [][]  = new long[h][w];
		dp[0][0] = 1;
		for(int i = 0; i<h; i++) {
			for(int j = 0; j<w; j++) {
				if(g[i][j] == '.') {
					if(i-1 >= 0)dp[i][j] = (dp[i][j] + dp[i-1][j])%mod;
					if(j-1 >= 0)dp[i][j] = (dp[i][j] + dp[i][j-1])%mod;
				}
			}
		}
		output.append(dp[h-1][w-1]);
		out.println(output);
	}
	
	public static void main(String[] args) {
		int t = 1;
		//t = fs.nextInt();
		for(int cs = 1; cs <= t; cs++) {
			solve();
		}
		out.close();
	}
	
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
	
	static int ceil(int x,int y) {
		return (x % y == 0 ? x / y : (x / y +1));
	}
	
	static long ceil(long x,long y) {
		return (x % y == 0 ? x / y : (x / y +1));
	}
	
	static int max(int x,int y) {
		return Math.max(x, y);
	}
	
	static int min(int x,int y) {
		return Math.min(x, y);
	}
	
	static long max(long x,long y) {
		return Math.max(x, y);
	}
	
	static long min(long x,long y) {
		return Math.min(x, y);
	}
	
	static int power(int x,int y) {
		int res = 1;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x);
			y >>= 1;
            x = (x * x);
		}
		return res;
	}
	
	static long power(long x,long y) {
		long res = 1;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x);
			y >>= 1;
            x = (x * x);
		}
		return res;
	}
	
	static long power(long x,long y,long mod) {
		long res = 1;
		x %= mod;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x) % mod;
			y >>= 1;
            x = (x * x) % mod;
		}
		return res;
	}
	
	static void intsort(int [] a) {
		List<Integer> temp = new ArrayList<Integer>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void longsort(long [] a) {
		List<Long> temp = new ArrayList<Long>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void reverseintsort(int [] a) {
		List<Integer> temp = new ArrayList<Integer>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		Collections.reverseOrder();
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void reverselongsort(long [] a) {
		List<Long> temp = new ArrayList<Long>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		Collections.reverseOrder();
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void intpairsort(intpair [] a) {
		List<intpair> temp = new ArrayList<intpair>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp,(p1,p2) -> {
			if(p1.x == p2.x) return p1.y >= p2.y ? -1 : 1;
			else return p1.x > p2.x ? -1 : 1;
		});
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void longpairsort(longpair [] a) {
		List<longpair> temp = new ArrayList<longpair>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp,(p1,p2) -> {
			if(p1.x == p2.x) return p1.y >= p2.y ? -1 : 1;
			else return p1.x > p2.x ? -1 : 1;
		});
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static class intpair{
		public int x;
		public int y;
		
		intpair(int a,int b){
			this.x = a;
			this.y = b;
		}
		
		intpair(){}
	}
	
	static class longpair{
		public long x;
		public long y;
		
		longpair(long a,long b){
			this.x = a;
			this.y = b;
		}
		
		longpair(){}
	}
	
	static class data{
		public long sum;
		
		data(long val){
		    this.sum = val;
		}
		
		data(){}
		
		data combine(data l, data r) {
		    data res = new data();
		    res.sum = l.sum + r.sum;
		    return res;
		}
	}
	
	static class Seg_Tree extends data{
		public int n;
		data [] seg;
		
		Seg_Tree(int sz){
			this.n = sz;
			seg = new data[4*n+4];
		}
		
		void build(long a[], int v, int tl, int tr) {
		    if (tl == tr) {
		        seg[v] = new data(a[tl]);
		    } else {
		        int tm = (tl + tr) / 2;
		        build(a, v*2, tl, tm);
		        build(a, v*2+1, tm+1, tr);
		        seg[v] = combine(seg[v*2],seg[v*2+1]);
		    }
		}

		void update(int v, int tl, int tr, int pos, long new_val) {
		    if (tl == tr) {
		        seg[v] = new data(new_val);
		    } else {
		        int tm = (tl + tr) / 2;
		        if (pos <= tm)
		            update(v*2, tl, tm, pos, new_val);
		        else
		            update(v*2+1, tm+1, tr, pos, new_val);
		        seg[v] = combine(seg[v*2],seg[v*2+1]);
		    }
		}
		
		data query(int v, int tl, int tr, int l, int r) {
		    if (l > r) 
		        return new data(0);
		    if (l == tl && r == tr) 
		        return seg[v];
		    int tm = (tl + tr) / 2;
		    return combine(query(v*2, tl, tm, l, min(r, tm)),query(v*2+1, tm+1, tr, max(l, tm+1), r));
		}
	}
	
	static class Bit_Tree{
		static int n;
		static int [] bit;
		
		Bit_Tree(int sz){
			Bit_Tree.n = sz;
			Bit_Tree.bit = new int[n+1];
		}
		
		static int child(int x) {
			return x + (x & (-x));
		}
		
		static int parent(int x) {
			return x - (x & (-x));
		}
		
		static void build(int [] a) {
			for(int i = 0; i<a.length; i++) {
				int start = i+1;
				while(start <= n) {
					bit[start] += a[i];
					start = child(start);
				}
			}
		}
		
		static void update(int idx,int new_val) {
			idx += 1;
			while(idx <= n) {
				bit[idx] += new_val;
				idx = child(idx);
			}
		}
		
		static int query(int right) {
			int res = 0;
			while(right > 0) {
				res += bit[right];
				right = parent(right);
			}
			return res;
		}
		
		static int query(int left,int right) {
			return query(right) - query(left-1);
		}
	}
}