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: Runtime Error)

/**
 *       Author:  kulubat
 *       Written on Tuesday, 14 April 2020.
 **/


#include <iostream>
#include <vector>


using namespace std;

const int mod = 1E9+7;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    
    int H, W, A, B;

    cin >> H >> W >> A >> B;

    vector<vector<int>> dp(H+1, vector<int>(W+1));

    dp[0][1] = 1;
    for(int i = 1; i <= H-A; ++i) {
        for(int j = 1; j <= W; ++j) {
            dp[i][j] = dp[i-1][j] +  dp[i][j-1];
            dp[i][j] %= mod;
        }
    }


    for(int i = H-A+1; i <= H; ++i) {
        for(int j = B+1; j <= W; ++j) {
            dp[i][j] = dp[i-1][j] +  dp[i][j-1];
            dp[i][j] %= mod;
        }
    }

    cout << dp[H][W] << "\n";
    return 0;
}