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)

/**
 *    author:  zjsdut
 *    created: 2020/01/19 10:57:55
**/
#include <bits/stdc++.h>

using namespace std;

struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
  };
} fast_ios_;

template<typename A, typename B>
bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template<typename A, typename B>
bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

template<typename T>
istream &operator>>(istream &stream, vector<T> &vec) {
  for (auto &x : vec) stream >> x;
  return stream;
}

void scan() {}

template<class T, class ...Args>
void scan(T &a, Args &...rest) {
  cin >> a;
  scan(rest...);
}

using ll = long long;
using vl = vector<ll>;
using vb = vector<bool>;
using vi = vector<int>;
using pii = pair<int, int>;
template<typename T> using vv = vector<vector<T>>;
#define rng(i, a, b) for(int i = (int)(a); i < (int)(b); ++i)
#define up(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define down(i, b, a) for (int i = int(b); i >= int(a); i--)
#define rep(n) for(int _iter_##n = 0, _num_##n = (int)n; _iter_##n < _num_##n; ++_iter_##n)
#define FOR(x, cont) for (const auto &x: cont)
#define For(x, cont) for (auto &x: cont)
#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int)(x).size()
#define UNIQ(vec) (vec).erase(unique(all(vec)), end(vec))
#define LB(cont, x) int(lower_bound(all(cont), x) - begin(cont))
#define UB(cont, x) int(upper_bound(all(cont), x) - begin(cont))

template<typename T>
ostream &operator<<(ostream &stream, const vector<T> &vec) {
  if (!vec.empty()) {
    stream << vec[0];
    for (size_t i = 1; i != vec.size(); ++i)
      stream << ' ' << vec[i];
  }
  return stream;
}

template<typename T>
void print(const vector<T> &t) { cout << t << '\n'; }

template<typename T>
void print(const vector<vector<T>> &t) {
  for (const auto &row : t) {
    print(row);
  }
}

template<typename T>
void print(const T &t) { cout << t << ' '; }

template<typename T, typename ...Args>
void print(const T &t, const Args &...rest) {
  print(t);
  print(rest...);
}

template<typename T>
void println(const T &t) { cout << t << '\n'; }

template<typename T, typename ...Args>
void println(const T &t, const Args &...rest) {
  print(t);
  println(rest...);
}
// tourist's modular-arithmetic class
template<typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template<typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}

  template<typename U>
  Modular(const U &x) {
    value = normalize(x);
  }

  template<typename U>
  static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type &operator()() const { return value; }

  template<typename U>
  explicit operator U() const { return static_cast<U>(value); }

  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }

  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }

  template<typename U>
  Modular &operator+=(const U &other) { return *this += Modular(other); }

  template<typename U>
  Modular &operator-=(const U &other) { return *this -= Modular(other); }

  Modular &operator++() { return *this += 1; }

  Modular &operator--() { return *this -= 1; }

  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }

  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }

  Modular operator-() const { return Modular(-value); }

  template<typename U = T>
  enable_if_t<is_same<typename Modular<U>::Type, int>::value, Modular> &operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
    "divl %4; \n\t"
    : "=a" (d), "=d" (m)
    : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }

  template<typename U = T>
  enable_if_t<is_same<typename Modular<U>::Type, int64_t>::value, Modular> &operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }

  template<typename U = T>
  enable_if_t<!is_integral<typename Modular<U>::Type>::value, Modular> &operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) { return *this *= Modular(inverse(other.value, mod())); }

  template<typename U>
  friend const Modular<U> &abs(const Modular<U> &v) { return v; }

  template<typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template<typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

 private:
  Type value;
};

template<typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value == rhs.value; }

template<typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) { return lhs == Modular<T>(rhs); }

template<typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) == rhs; }

template<typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value < rhs.value; }

template<typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template<typename T>
bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template<typename T>
string to_string(const Modular<T> &number) {
  return to_string(number());
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template<typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = 1000000007;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

template<typename T>
class Binom {
  vector<T> fact_, inv_fact_;
 public:
  explicit Binom(int n) : fact_(n + 1), inv_fact_(n + 1) {
    fact_[0] = 1;
    up (i, 1, n) fact_[i] = fact_[i - 1] * i;
    inv_fact_[n] = 1 / fact_[n];
    down (i, n, 1) {
      inv_fact_[i - 1] = inv_fact_[i] * i;
    }
  }

  T binom(int x, int y) const {
    if (x < 0 || y < 0) return 0;
    if (x < y) return 0;
    assert(x < SZ(fact_));
    return fact_[x] * inv_fact_[y] * inv_fact_[x - y];
  }

  T fact(int n) const {
    assert(n >= 0 && n < SZ(fact_));
    return fact_[n];
  }

  T inv_fact(int n) const {
    assert(n >= 0 && n < SZ(inv_fact_));
    return inv_fact_[n];
  }
};
// debug code by tourist
string to_string(const string &s) {
  return '"' + s + '"';
}

string to_string(const char *s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

template<typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template<typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

void debug_out() { cerr << endl; }

template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

int main() {
#if defined LOCAL
  ifstream in("in.txt");
  cin.rdbuf(in.rdbuf());
#endif
  int h, w, a, b;
  scan(h, w, a, b);
  Binom<Mint> B(h + w);
  auto calc = [&](int H, int W) {
    return B.binom(H + W, H);
  };
  Mint ans = 0;
  debug(w - b - 1, a);
  auto t = calc(w - b - 1, a);
  debug(t);
  if (a + 1 == h) {
    println(t);
    return 0;
  }
  rng (i, 0, w) {
    if (i < b) {
      ans += calc(i, h - a - 2) * t;
    } else {
      ans += calc(i, h - a -2) * calc(a, w - 1 - i);
    }
//    debug(ans);
  }
  println(ans);
  return 0;
}