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 9.2.1) (judge verdict: Accepted)

#define LOCAL
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;

#define rep(i,s,n) for (int i = (ll)s; i < (ll)n; i++)
#define rrep(i,n,e) for (int i = (ll)n; i > (ll)e; i--)
#define ll long long
#define ld long double
#define pb push_back
#define eb emplace_back
#define All(x) x.begin(), x.end()
#define Range(x, i, j) x.begin() + i, x.begin() + j
#define lbidx(x, y) lower_bound(x.begin(), x.end(), y) - x.begin()
#define ubidx(x, y) upper_bound(x.begin(), x.end(), y) - x.begin()
#define llbidx(x, y, z) lower_bound(x.begin(), x.end(), z) - lower_bound(x.begin(), x.end(), y) // dist between two elements
// #define M_PI 3.14159265358979323846 // CF
#define deg2rad(deg) ((((double)deg)/((double)360)*2*M_PI))
#define rad2deg(rad) ((((double)rad)/(double)2/M_PI)*(double)360)
#define Find(set, element) set.find(element) != set.end()
#define Decimal(x) cout << fixed << setprecision(10) << x << endl; // 小数点を10桁まで表示
#define endl "\n"
#define Case(x) printf("Case #%d: ", x); // gcj

typedef pair<int, int> PI;
typedef pair<ll, ll> PLL;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<vector<vector<int>>> vvvi;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef vector<vector<vector<ll>>> vvvl;
typedef vector<PI> vpi;
typedef vector<vector<PI>> vvpi;
typedef vector<PLL> vpl;
typedef vector<vector<PLL>> vvpl;
typedef vector<char> vch;
typedef vector<vector<char>> vvch;

constexpr ll LINF = 1001002003004005006ll;
constexpr int INF = 1001001001;
constexpr int n_max = 2e5+10;

template<class T>
inline bool chmax(T &a, T b) { if(a<b) { a=b; return true; } return false; };
template<class T>
inline bool chmin(T &a, T b) { if(a>b) { a=b; return true; } return false; };

template<class T, class U>
T POW(T x, U n) {T ret=1; while (n>0) {if (n&1) {ret*=x;} x*=x; n>>=1;} return ret;};

// debug
template <typename A, typename B>
string to_string(pair<A, B> p);
string to_string(const string &s) {return '"' + s + '"';};
string to_string(const char c) {return to_string((string) &c);};
string to_string(bool b) {return (b ? "true" : "false");};
template <size_t N>
string to_string(bitset<N> v){
  string res = "";
  for(size_t i = 0; i < N; i++) res += static_cast<char>('0' + v[i]);
  return res;
};
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;
};
template <typename A, typename B>
string to_string(pair<A, B> p){return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";}

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(...) 71
#endif

void print() { cout << endl; }
template <class Head, class... Tail>
void print(Head&& head, Tail&&... tail) {
  cout << head;
  if (sizeof...(tail) != 0) cout << " ";
  print(forward<Tail>(tail)...);
};

template <class T>
void print(vector<T> &vec) {
  for (auto& a : vec) {
    cout << a;
    if (&a != &vec.back()) cout << " ";
  }
  cout << endl;
};

template <class T>
void print(vector<vector<T>> &df) {
  for (auto& vec : df) {
    print(vec);
  }
};

template<std::int_fast64_t Modulus>
class modint {
  using i64 = int_fast64_t;

  public:
  i64 a;

  constexpr modint(const i64 x = 0) noexcept {
    this -> a = x % Modulus;
    if(a < 0){
      a += Modulus;
    }
  }
  // constexpr i64 &value() const noexcept {return a;}
  constexpr const i64 &value() const noexcept {return a;}
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if(a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if(a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    i64 a_ = rhs.a, b = Modulus, u = 1, v = 0;
    while(b){
      i64 t = a_/b;
      a_ -= t * b; swap(a_,b);
      u -= t * v; swap(u,v);
    }
    a = a * u % Modulus;
    if(a < 0) a += Modulus;
    return *this;
  }

  constexpr bool operator==(const modint rhs) noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint rhs) noexcept {
    return a != rhs.a;
  }
  constexpr bool operator>(const modint rhs) noexcept {
    return a > rhs.a;
  }
  constexpr bool operator>=(const modint rhs) noexcept {
    return a >= rhs.a;
  }
  constexpr bool operator<(const modint rhs) noexcept {
    return a < rhs.a;
  }
  constexpr bool operator<=(const modint rhs) noexcept {
    return a <= rhs.a;
  }
  // constexpr modint& operator++() noexcept {
  //     return (*this) += modint(1);
  // }
  // constexpr modint operator++(int) {
  //     modint tmp(*this);
  //     operator++();
  //     return tmp;
  // }
  // constexpr modint& operator--() noexcept {
  //     return (*this) -= modint(1);
  // }
  // constexpr modint operator--(int) {
  //     modint tmp(*this);
  //     operator--();
  //     return tmp;
  // }
  template<typename T>
  friend constexpr modint modpow(const modint &mt, T n) noexcept {
    if(n < 0){
      modint t = (modint(1) / mt);
      return modpow(t, -n);
    }
    modint res = 1, tmp = mt;
    while(n){
      if(n & 1)res *= tmp;
      tmp *= tmp;
      n /= 2;
    }
    return res;
  }
};

const long long MOD = 1e9+7;
using mint = modint<MOD>;
// iostream
std::ostream &operator<<(std::ostream &out, const modint<MOD> &m) {
  out << m.a; return out;
};
std::istream &operator>>(std::istream &in, modint<MOD> &m) {
  long long a; in >> a; m = mint(a); return in;
};

mint fact[200005];

void init() {
  fact[0] = mint(1);
  for(int i = 1; i < 200005; i++) {
    fact[i] = fact[i-1] * mint(i);
  }
};

// calculate nCr mod
mint modcomb(long long n, long long r) {
  return fact[n] / fact[r] / fact[n - r];
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int H, W, A, B; cin >> H >> W >> A >> B;
  mint ans = mint(0);
  init();

  rep(i, B, W) {
    int h1 = H-A-1;
    int w1 = i;
    mint hw = modcomb(h1+w1, h1);
    int h2 = A-1;
    int w2 = W-i-1;
    mint hw2 = modcomb(h2+w2, h2);
    ans += hw * hw2;
  }

  cout << ans << endl;


  return 0;
};