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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>

const int mod = 1e9 + 7;

void swap(long long* a, long long* b){
  *a ^= *b;
  *b ^= *a;
  *a ^= *b;
}

long long inverse(long long x){
  long long m = mod, u = 1, v = 0;
  while(m){
    long long t = x / m;
    x -= t * m; swap(&x, &m);
    u -= t * v; swap(&u, &v);
  }
  u %= mod;
  if(u < 0) u += mod;
  return u;
}

int main(){
  long long H, W, A, B;
  scanf("%lld%lld%lld%lld", &H, &W, &A, &B);
  
  long long fact[H + W + 1];
  fact[0] = 1;
  for(int k = 1; k <= H + W; k++){
    fact[k] = fact[k - 1] * k % mod;
  }
  
  long long move = 0;
  for(long long j = B; j < W; j++){
    move += 
      fact[H - A - 1 + j] * inverse(fact[j] * fact[H - A - 1] % mod) % mod
      * fact[W - j + A - 2] % mod * inverse(fact[W - j - 1] * fact[A - 1] % mod) % mod;
    move %= mod;
  }
  
  printf("%lld\n", move);
  
  return 0;
}