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 (5.6.30) (judge verdict: Wrong Answer)

<?php
$s=fgets(STDIN);
list($h,$w,$a,$b)=explode(' ',$s);
$h=(int)$h;
$w=(int)$w;
$a=(int)$a;
$b=(int)$b;
for($i=$h;$i>0;$i--) $dp[$i][$w]=1;
for($i=$w;$i>$b;$i--) $dp[$h][$i]=1;
for($i=$w-1;$i>$b;$i--){
    for($j=$h-1;$j>0;$j--)
        $dp[$j][$i]=$dp[$j+1][$i]+$dp[$j][$i+1];
}
$t=$h-$a+1;
for($i=1;$i<=$b;$i++) $dp[$t][$i]=0;
for($i=$b;$i>0;$i--){
    for($j=$h-$a;$j>0;$j--)
        $dp[$j][$i]=$dp[$j+1][$i]+$dp[$j][$i+1];
}
fwrite(STDOUT,$dp[1][1]%(1e9+7));
?>