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
fscanf(STDIN, "%d %d %d %d", $h, $w, $a, $b);

for($j = 1; $j <= $h - $a -1; $j++){
    $dp[0][$j] = 1;
}
for($i = 1; $i < $w; $i++){
    $dp[$i][0] = 1;
}

for($x = 1; $x <= $w - 1; $x++){
    for($y = 1; $y <= $h - $a - 1; $y++){
        $dp[$x][$y] = $dp[$x-1][$y] + $dp[$x][$y-1];
        unset($dp[$x-1][$y-1]);
    }
}

for($i = 0; $i <= $a - 1; $i++){
    $dp[$b][$h-$a+$i] = $dp[$b][$h-$a-1];
}
for($x = $b + 1; $x <= $w - 1; $x++){
    for($y = $h - $a; $y <= $h - 1; $y++){
        $dp[$x][$y] = $dp[$x-1][$y] + $dp[$x][$y-1];
    }
}
$answer = $dp[$w-1][$h-1] % (10**9 + 7);
print $answer;