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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)] use proconio::{input, marker::{Bytes, Chars, Usize1, Isize1}};
#[allow(unused_imports)] use std::cmp::{min, max};
#[allow(unused_imports)] use superslice::Ext as _;

const MAX: usize = 200000;
const MOD: usize = 1000000007;

fn com_init( fac: &mut [usize], finv: &mut [usize] )
{
	let mut inv = [0usize; MAX];
	fac[0] = 1;
	fac[1] = 1;
	finv[0] = 1;
	finv[1] = 1;
	inv[1] = 1;
	for i in 2..MAX {
		fac[i] = fac[i-1] * i % MOD;
		inv[i] = MOD - inv[MOD%i] * (MOD /i) % MOD;
		finv[i] = finv[i-1] * inv[i] % MOD;
	}

}

fn com( n: usize, k: usize, fac: &[usize], finv: &[usize] ) -> usize {
	if n < k {
		return 0;
	}
	return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD;
}

#[proconio::fastout]
fn main() {
	input! {
		h: usize,
		w: usize,
		a: usize,
		b: usize,
	}

	// C(n,r)前処理
	let mut fac = [0usize; MAX];
	let mut finv = [0usize; MAX];
	com_init(&mut fac, &mut finv );

	// 必ず通るマス (H-A-1, B～W-1)
	let mut ans = 0;
	for i in b..w {
		// (0, 0)->(H-A-1, W-i-1)の経路
		let a1 = com(h-a-1+i, i, &fac, &finv);
		// そこから->(H-1, W-1)の経路
		let a2 = com(a+w-1-i-1, w-1-i, &fac, &finv);
		ans += a1 * a2 % MOD;
		ans %= MOD;
	}

	println!("{}", ans);
}