Problem:
Score : 400 points

Problem Statement

We have a large square grid with H rows and W columns.
Iroha is now standing in the top-left cell.
She will repeat going right or down to the adjacent cell, until she reaches the bottom-right cell.

However, she cannot enter the cells in the intersection of the bottom A rows and the leftmost B columns. (That is, there are A×B forbidden cells.) There is no restriction on entering the other cells.

Find the number of ways she can travel to the bottom-right cell.

Since this number can be extremely large, print the number modulo 10^9+7.

Constraints

1 ≦ H, W ≦ 100,000

1 ≦ A < H

1 ≦ B < W

Input

The input is given from Standard Input in the following format:

H W A B

Output

Print the number of ways she can travel to the bottom-right cell, modulo 10^9+7.

Sample Input 1

2 3 1 1

Sample Output 1

2

We have a 2×3 grid, but entering the bottom-left cell is forbidden. The number of ways to travel is two: "Right, Right, Down" and "Right, Down, Right".

Sample Input 2

10 7 3 4

Sample Output 2

3570

There are 12 forbidden cells.

Sample Input 3

100000 100000 99999 99999

Sample Output 3

1

Sample Input 4

100000 100000 44444 55555

Sample Output 4

738162020

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::str::FromStr;

fn main() {
	let m = 1000000007i64;
	let hwab = read_vec_i32();
	let (h, w, a, b) = (hwab[0], hwab[1], hwab[2], hwab[3]);
	let mut f = vec![0i64; (h + w + 1) as usize];
	let mut rf = vec![0i64; (h + w + 1) as usize];
	f[0] = 1;
	rf[0] = 1;
	for i in 1..h+w+1 {
		f[i as usize] = f[(i - 1) as usize] * (i as i64) % m;
		rf[i as usize] = pow(f[i as usize], m - 2, m)
	}
	let cmb = |x: i32, y: i32, m: i64| -> i64 {
		f[(x + y) as usize] * rf[x as usize] % m * rf[y as usize] % m
	};
	let ans = (0..h-a).map(|y| cmb(b - 1, y, m) * cmb(w - b - 1, h - y - 1, m)).fold(0i64, |x, y| (x + y) % m);
	println!("{}", ans);
}

fn pow(x: i64, n: i64, m: i64) -> i64 {
	if n > 0 {
		let a = pow(x, n / 2, m);
		let b = a * a % m;
		if n & 1 != 0 { b * x % m } else { b }
	} else { 1 }
}

fn read_vec_i32() -> Vec<i32> {
	let mut line = String::new();
	std::io::stdin().read_line(&mut line).unwrap();
	line.trim().split_whitespace().map(|str| i32::from_str(str).unwrap()).collect()
}