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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case, unused)]
use std::collections::*;

////////// missing functions in 1.15.1 //////////
macro_rules! eprint {
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = write!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! eprintln {
	() => { eprintln!(""); };
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = writeln!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! dbg {
	($v:expr) => {{
		let val = $v;
		eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
		val
	}}
}
/////////////////////////////////////////////////
pub trait SetMinMax {
	fn setmin(&mut self, v: Self) -> bool;
	fn setmax(&mut self, v: Self) -> bool;
}
impl<T> SetMinMax for T where T: PartialOrd {
	fn setmin(&mut self, v: T) -> bool {
		*self > v && { *self = v; true }
	}
	fn setmax(&mut self, v: T) -> bool {
		*self < v && { *self = v; true }
	}
}

macro_rules! mat {
	($($e:expr),*) => { Vec::from(vec![$($e),*]) };
	($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
	($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
	($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

#[macro_export]
macro_rules! ok {
	($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
		$a$([$i])*.$f($($t),*)
	};
	($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
		let t = $e;
		ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
	} };
}

pub fn readln() -> String {
	let mut line = String::new();
	::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
	line
}

macro_rules! read {
	($($t:tt),*; $n:expr) => {{
		let stdin = ::std::io::stdin();
		let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
			let line = line.unwrap();
			let mut it = line.split_whitespace();
			_read!(it; $($t),*)
		}).collect::<Vec<_>>();
		ret
	}};
	($($t:tt),*) => {{
		let line = readln();
		let mut it = line.split_whitespace();
		_read!(it; $($t),*)
	}};
}

macro_rules! _read {
	($it:ident; [char]) => {
		_read!($it; String).chars().collect::<Vec<_>>()
	};
	($it:ident; [u8]) => {
		Vec::from(_read!($it; String).into_bytes())
	};
	($it:ident; usize1) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
	};
	($it:ident; [usize1]) => {
		$it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
	};
	($it:ident; [$t:ty]) => {
		$it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
	};
	($it:ident; $t:ty) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
	};
	($it:ident; $($t:tt),+) => {
		($(_read!($it; $t)),*)
	};
}

pub fn main() {
	let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

use std::ops::*;
use std::marker::PhantomData;

pub trait Int {
	fn as_i32(self) -> i32;
	fn as_i64(self) -> i64;
	fn as_u32(self) -> u32;
	fn as_u64(self) -> u64;
	fn as_usize(self) -> usize;
}

macro_rules! impl_int {
	() => {};
	($t:ty $(, $ts:ty)*) => {
		impl Int for $t {
			fn as_i32(self) -> i32 {
				self as i32
			}
			fn as_i64(self) -> i64 {
				self as i64
			}
			fn as_u32(self) -> u32 {
				self as u32
			}
			fn as_u64(self) -> u64 {
				self as u64
			}
			fn as_usize(self) -> usize {
				self as usize
			}
		}
		impl_int!($($ts),*);
	}
}

impl_int!(i8, i16, i32, i64, u8, u16, u32, u64, isize, usize);

pub trait Mod: Copy + Default + Ord {
	fn m() -> u32;
}

#[derive(Clone, Copy, Default, Hash, PartialEq, PartialOrd, Eq, Ord)]
pub struct ModP<M>(pub u32, PhantomData<M>);

impl<M> ::std::fmt::Debug for ModP<M> {
	fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
		self.0.fmt(f)
	}
}

impl<M> ::std::fmt::Display for ModP<M> {
	fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
		self.0.fmt(f)
	}
}

impl<M: Mod> ModP<M> {
	/// Assume 0 <= a < m.
	pub fn new<I: Int>(a: I) -> ModP<M> {
		ModP(a.as_u32(), PhantomData)
	}
	pub fn pow<I: Int>(&self, b: I) -> ModP<M> {
		let mut b = b.as_i64();
		if b < 0 {
			b = b % (M::m() - 1) as i64 + M::m() as i64 - 1;
		}
		let mut res = ModP::new(1);
		let mut a = *self;
		while b > 0 {
			if (b & 1) > 0 { res *= a; }
			a *= a;
			b >>= 1;
		}
		res
	}
	pub fn inv(&self) -> ModP<M> {
		self.pow(M::m() as u64 - 2)
	}
}

impl<'a, M: Mod> Add for &'a ModP<M> {
	type Output = ModP<M>;
	fn add(self, a: &ModP<M>) -> ModP<M> {
		let v = self.0 + a.0;
		if v >= M::m() { ModP::new(v - M::m()) } else { ModP::new(v) }
	}
}

impl<'a, M: Mod> Sub for &'a ModP<M> {
	type Output = ModP<M>;
	fn sub(self, a: &ModP<M>) -> ModP<M> {
		if self.0 < a.0 { ModP::new(M::m() - a.0 + self.0) } else { ModP::new(self.0 - a.0 ) }
	}
}

impl<'a, M: Mod> Mul for &'a ModP<M> {
	type Output = ModP<M>;
	fn mul(self, a: &ModP<M>) -> ModP<M> {
		ModP::new(((self.0 as u64 * a.0 as u64) % M::m() as u64) as u32)
	}
}

impl<'a, M: Mod> Div for &'a ModP<M> {
	type Output = ModP<M>;
	fn div(self, a: &ModP<M>) -> ModP<M> {
		self * a.inv()
	}
}

impl<'a, M: Mod> Neg for &'a ModP<M> {
	type Output = ModP<M>;
	fn neg(self) -> ModP<M> {
		ModP::new(if self.0 == 0 { 0 } else { M::m() - self.0 })
	}
}

impl<M: Mod> Neg for ModP<M> {
	type Output = ModP<M>;
	fn neg(self) -> ModP<M> {
		(&self).neg()
	}
}

macro_rules! impl_all {
	($t:ident$(<$($g:ident),*>)*; $Op:ident:$op:ident:$Opa:ident:$opa:ident) => {
		impl<$($($g),*)*> $Op for $t$(<$($g),*>)* where for<'b> &'b $t$(<$($g),*>)*: $Op<Output = $t$(<$($g),*>)*> {
			type Output = $t$(<$($g),*>)*;
			fn $op(self, a: $t$(<$($g),*>)*) -> $t$(<$($g),*>)* { (&self).$op(&a) }
		}
		impl<'a, $($($g),*)*> $Op<&'a $t$(<$($g),*>)*> for $t$(<$($g),*>)* where for<'b> &'b $t$(<$($g),*>)*: $Op<Output = $t$(<$($g),*>)*> {
			type Output = $t$(<$($g),*>)*;
			fn $op(self, a: &$t$(<$($g),*>)*) -> $t$(<$($g),*>)* { (&self).$op(&a) }
		}
		impl<'a, $($($g),*)*> $Op<$t$(<$($g),*>)*> for &'a $t$(<$($g),*>)* where for<'b> &'b $t$(<$($g),*>)*: $Op<Output = $t$(<$($g),*>)*> {
			type Output = $t$(<$($g),*>)*;
			fn $op(self, a: $t$(<$($g),*>)*) -> $t$(<$($g),*>)* { (&self).$op(&a) }
		}
		impl<$($($g),*)*> $Opa for $t$(<$($g),*>)* where for<'b> &'b $t$(<$($g),*>)*: $Op<Output = $t$(<$($g),*>)*> {
			fn $opa(&mut self, a: $t$(<$($g),*>)*) { *self = (&*self).$op(&a) }
		}
	}
}

impl_all!(ModP<M>; Add:add:AddAssign:add_assign);
impl_all!(ModP<M>; Sub:sub:SubAssign:sub_assign);
impl_all!(ModP<M>; Mul:mul:MulAssign:mul_assign);
impl_all!(ModP<M>; Div:div:DivAssign:div_assign);

#[macro_export]
macro_rules! define_mod {
	($name:ident; $e:expr) => {
		#[derive(Clone, Copy, Default, Hash, PartialEq, PartialOrd, Eq, Ord)]
		pub struct _Mod;
		pub type $name = $crate::ModP<_Mod>;
		impl $crate::Mod for _Mod {
			fn m() -> u32 { $e }
		}
	}
}

impl<M: Mod, I: Int> From<I> for ModP<M> {
	/// Assume 0 <= a < m.
	fn from(a: I) -> ModP<M> { ModP::new(a) }
}


fn run() {
	let (N, M) = read!(usize, usize);
	let cs = read!([char]; N);
	let mut dp = mat![P::new(0); N; M];
	define_mod!(P; 1_000_000_007);
	dp[0][0] = P::new(1);
	for i in 0..N {
		for j in 0..M {
			if i + 1 < N && cs[i + 1][j] == '.' {
				dp[i + 1][j] += dp[i][j];
			}
			if j + 1 < M && cs[i][j + 1] == '.' {
				dp[i][j + 1] += dp[i][j];
			}
		}
	}
	println!("{}", dp[N - 1][M - 1]);
}