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: Accepted)

// clang-format off
#include <bits/stdc++.h>
#define int long long
#define main signed main()
// #define main int main()
#define loop(i, a, n) for (int i = (a); i < (n); i++)
#define rep(i, n) loop(i, 0, n)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define prec(n) fixed << setprecision(n)
#define stlice(from, to) substr(from, (to) - (from) + 1)
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
using namespace std;
using pii = pair<int, int>;
using vi = vector<int>;
using vd = vector<double>;
using vc = vector<char>;
using vb = vector<bool>;
using vs = vector<string>;
using vpii = vector<pii>;
using vvi = vector<vi>;
using vvb = vector<vb>;
using vvpii = vector<vpii>;
template<typename A> using fn = function<A>;
constexpr int INF = sizeof(int) == sizeof(long long) ? 1000000000000000000LL : 1000000000;
constexpr int MOD = 1000000007;
constexpr double PI = acos(-1);
template<typename A, typename B> bool cmin(A &a, const B &b) { return a > b ? (a = b, true) : false; }
template<typename A, typename B> bool cmax(A &a, const B &b) { return a < b ? (a = b, true) : false; }
constexpr bool odd(const int &n) { return n & 1; }
constexpr bool even(const int &n) { return !odd(n); }
void solve();
main { solve(); return 0; }
// clang-format on

constexpr int powm(int a, int b, const int& m) {
  int c = 1;
  while (b) {
    if (odd(b)) c = (c * a) % m;
    b >>= 1;
    a = (a * a) % m;
  }
  return c;
}
struct modint {
  int v;
  modint(int a = 0)
    : v(((a % MOD) + MOD) % MOD) {
  }
  modint operator+(const modint& b) const {
    return (v + b.v) % MOD;
  }
  modint operator-(const modint& b) const {
    return (v - b.v + MOD) % MOD;
  }
  modint operator*(const modint& b) const {
    return (v * b.v) % MOD;
  }
  modint operator/(const modint& b) const {
    return (v * powm(b.v, MOD - 2, MOD)) % MOD;
  }
};
bool operator==(const modint& a, const modint& b) {
  return a.v == b.v;
}
modint& operator+=(modint& a, const modint& b) {
  return a = a + b;
}
modint& operator-=(modint& a, const modint& b) {
  return a = a - b;
}
modint& operator*=(modint& a, const modint& b) {
  return a = a * b;
}
modint& operator/=(modint& a, const modint& b) {
  return a = a / b;
}

ostream& operator<<(ostream& out, const modint& a) {
  return out << a.v;
}
istream& operator>>(istream& in, modint& a) {
  int v;
  in >> v;
  a = modint(v);
  return in;
}

void solve() {
  int h, w, a, b;
  cin >> h >> w >> a >> b;
  vector<modint> factorial(h + w);
  factorial[0] = 1;
  loop(i, 1, factorial.size()) factorial[i] = modint(i) * factorial[i - 1];
  auto ncr = [&](const int& n, const int& r) {
    return factorial[n] / (factorial[n - r] * factorial[r]);
  };
  auto ways = [&](const int& c, const int& r) {
    return ncr(c + r, c);
  };
  modint s = 0;
  loop(i, b, w) s += ways(h - a - 1, i) * ways(a - 1, w - 1 - i);
  cout << s << endl;
}