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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(long long int i=0; i<n; i++)
int main(){
    int H, W, A, B; cin >> H >> W >> A >> B;
    long long int mod = pow(10,9) + 7;

    vector<vector<long long int>> c(2, vector<long long int>(W+1,0));
  	c[0][0] = 0; c[0][1] = 1;
    for(int i=1; i<=H; i++){
      	//cout << c[i%2][0] << " ";
        for(int j=1; j<=W; j++){
            if(i >= H-A+1 && j <= B+1) c[i%2][j] = c[(i+1)%2][j];
            else c[i%2][j] = c[(i+1)%2][j] + c[i%2][j-1];
          	//cout << c[i%2][j] << " ";
        }
     	//cout << endl;
    }
    cout << c[H%2][W] % mod << endl;
}