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
$line = fgets(STDIN);
$hwab = explode(' ', trim($line));
$h = $hwab[0];
$w = $hwab[1];
$a = $hwab[2];
$b = $hwab[3];

$count = 0;
for ($i = $b; $i < $w ;$i++) {
    $n1 = $h - $a - 1 + $i;
    $r1 = $i;
    $c1 = gmp_fact($n1) / (gmp_fact($r1) * gmp_fact($n1-$r1));
    $n2 = $w - $i - 1 + $a - 1;
    $r2 = $w - $i - 1;
    if ($r2 === 0) {
        $c2 = 1;
    } else {
        $c2 = gmp_fact($n2) / (gmp_fact($r2) * gmp_fact($n2-$r2));
    }
    $count = $count + $c1 * $c2;
}
echo $count;

function gmp_fact($num){
    if($num>0) {
        return $num *= gmp_fact($num-1);
    }
    return 1;
}