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)

#include <iostream>
#include <string>
#define int long long
using namespace std;
const int MOD = 1e9+7;
 
int pot(int x, int p) {
if (p == 0) return 1;
int z = pot(x, p/2);
z = (z*z)%MOD;
if (p%2) z = (z*x) % MOD;
return z;
}
 
int inv(int x) {
return pot(x, MOD-2);
}
 
int pows[20000 + 10];
int powsinv[20000 + 10];
 
int calc(int a, int b) {
int x = pows[a+b-2] * powsinv[a-1] % MOD;
x = x * powsinv[b-1] % MOD;
return x;
}
 int a,b,w,h;
signed main(){
cin >> h >> w >> a >> b;
pows[0] = 1; powsinv[0] = 1;
for (int i = 1; i < 20000 + 10; i++) {
pows[i] = (pows[i-1] * i) % MOD;
powsinv[i] = inv(pows[i]);
}
 
int res = 0;
for (int i = b+1; i <= w; i++) {
  int x = calc(h - a, i) * calc(a, w-i+1) % MOD; 
  res = (res + x) % MOD;
}
 
cout << res << "\n";
return 0;
}