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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

$args = [];
while(true){
	$input = explode(' ', trim(fgets(STDIN)));
	foreach ($input as $value) {
		if ($value !== '') {
			$args[] = $value;
		}
		if (count($args) >= 4) {
			break;
		}
	}
	if (count($args) >= 4) {
		break;
	}
}

$tate = (int)$input[0];
$yoko = (int)$input[1];
$shita = (int)$input[2];
$hidari =(int)$input[3];

$row1 = route($tate - $shita, $yoko);
for ($i=$tate - $shita + 1; $i <=$tate ; $i++) { 
	for ($j=$hidari+1; $j <= $yoko; $j++) { 
		if ($i == $tate - $shita + 1) {
			$pre_rt = $row1;
		}
		if ($j==$hidari+1) {
			$rt[$i][$j] = $pre_rt[$i-1][$j];
		}else{
			$rt[$i][$j] = $pre_rt[$i-1][$j] + $rt[$i][$j-1];
		}
	}
	$pre_rt = $rt;
	$rt = null;
}
echo $pre_rt[$tate][$yoko] % 1000000007;


function route($tate, $yoko){
	for ($i=1; $i <=$tate ; $i++) {
		$rt[$i][1] = 1;
		for ($j=1; $j <=$yoko ; $j++) { 
			if ($i == 1) {
				$pre_rt[$i][$j] = 1;
				$rt[$i][$j] = 1;
			}else{
				if ($j == 1) {
					$rt[$i][$j] = 1;
				}else{
					$rt[$i][$j] = $pre_rt[$i-1][$j] + $rt[$i][$j-1];
				}
			}
		}
		$pre_rt = $rt;
		$rt = null;
	}
	return $pre_rt;
}