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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

'use strict';
function Main(input) {
const ary = (input.split(" ")).map(str => Number(str));
  const h = ary[0];
  const w = ary[1];
  const a = ary[2];
  const b = ary[3];
let wid = [];
for (let i=0; i<w; i++) {
  wid.push(1);
}
for (let j=0; j<h-a-1; j++) {
  for(let i=0; i<w-1; i++) {
    wid[i+1] += wid[i];
  }
}
wid.splice(0,b);
for (let j=0; j<a; j++) {
  for(let i=0; i<w-b-1; i++) {
    wid[i+1] += wid[i];
  }
}
if (wid[w-b-1] <1000000000) {
   console.log(wid[w-b-1]);
} else {
   console.log(wid[w-b-1] % (1000000000+7));
}
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));