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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.*;


public class Main {
  static int H, W, A, B;
  static int[][] dp;

  public static boolean isAllowed(int y, int x) {
    return (0 <= y && y < H && 0 <= x && x < W) && !(H - A <= y && x < B);
  }

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);

    H = sc.nextInt();
    W = sc.nextInt();
    A = sc.nextInt();
    B = sc.nextInt();

    dp = new int[H][W];
    dp[0][0] = 1;
    for(int i = 0; i < H; i++) {
      for(int j = 0; j < W; j++) {
        if(isAllowed(i, j)) {
          dp[i][j] += (isAllowed(i - 1, j) ? dp[i - 1][j] : 0) + (isAllowed(i, j - 1) ? dp[i][j - 1] : 0);
        }
      }
    }

    System.out.println(dp[H - 1][W - 1]);
  }
}