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 PHP (7.4.4) (judge verdict: Accepted)

<?php
  list($h, $w, $a, $b) = explode(" ", trim(fgets(STDIN)));

  $m = 1000000007;
  $middle = [];
  $ans = 0;

  $factorial = [];

  $factorial[0] = 1;
  for ($i=1; $i<=$w+$h; $i++) {
    $factorial[$i] = $i * $factorial[$i-1] % $m;
  }

  for ($i=$b+1; $i<=$w; $i++) {
    $ptn = combination2($i-1+$h-$a-1, $i-1, $m, $factorial);
    $ptn *= combination2($w-$i+$a-1, $w-$i, $m, $factorial)%$m;
    $ans += $ptn%$m;
  }
  echo $ans%$m;


/**
 * mod Pの世界での繰り返し二乗法
 * @param $b 基数
 * @param $p 指数
 * @param $m 素数
 */
function repeatSqrt($b, $p, $m){
  if($p==1)
  {
    return $b;
  }
  else if($p%2 == 0)
  {
    $t = repeatSqrt($b, floor($p/2), $m);
    return ($t * $t) % $m;
  }
  else
  {
    return ($b * repeatSqrt($b, $p-1, $m)) % $m;
  }
}

/**
 * mod Pの世界での組み合わせ(nCa)
 * @param $n 全体の数
 * @param $a 選択する数
 * @param $m 素数
 */
function combination($n, $a, $m)
{
    $x=1; // bunbo
    $y=1; // bunshi
    for($i=0;$i<$a;$i++)
    {
        $x=$x*($n-$i)%$m;
        $y=$y*($i+1)%$m;
    }
    // フェルマーの小定理 
    // Y^(P-1)≡1 (mod P) より
    // Y^(P-2)≡1/Y (mod P)
    // つまり
    // $x / $y = $x * $y^($m-2) (mod P)
    $y=repeatSqrt($y, $m-2, $m);
    return ($x*$y)%$m;
}


/**
 * mod Pの世界での組み合わせ(nCa)
 * @param $n 全体の数
 * @param $a 選択する数
 * @param $m 素数
 * @param $factorial 処理済みの階乗
 */
function combination2($n, $a, $m, $factorial)
{
    $x=$factorial[$n]; // bunbo
    $y=$factorial[$a]*$factorial[$n-$a]%$m; // bunshi

    // フェルマーの小定理 
    // Y^(P-1)≡1 (mod P) より
    // Y^(P-2)≡1/Y (mod P)
    // つまり
    // $x / $y = $x * $y^($m-2) (mod P)
    $y=repeatSqrt($y, $m-2, $m);
    return ($x*$y)%$m;
}