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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;
using Enu = System.Linq.Enumerable;

public class Program
{
    static readonly int Mod = (int)1e9 + 7;
    static void Add(ref int a, int b) { if ((a += b) >= Mod) a -= Mod; }

    public void Solve()
    {
        int H = Reader.Int(), W = Reader.Int(), A = Reader.Int(), B = Reader.Int();
        var C = new ModC(H + W, Mod);
        int ans = 0;
        long last = 0;

        for (int x = B; x < W; x++)
        {
            int h1 = H - A - 1;
            int w1 = x;
            int h2 = A;
            int w2 = W - x - 1;
            long a = C[h1 + w1, w1], b = C[h2 + w2, w2];
            if (last > 0) a = a + Mod - last;
            last = C[h1 + w1, w1];
            Add(ref ans, (int)(a * b % Mod));
        }
        Console.WriteLine(ans);
    }

    class ModC
    {
        readonly long P;
        readonly long[] Fact, InvFact;

        public int this[int n, int k]
        {
            get
            {
                if (n < 0 || k < 0 || k > n) return 0;
                return (int)(Fact[n] * InvFact[k] % P * InvFact[n - k] % P);
            }
        }
        public ModC(int maxN, int p) // maxN < p, p is prime
        {
            P = p;
            Fact = new long[maxN + 1];
            InvFact = new long[maxN + 1];
            Fact[0] = InvFact[0] = 1;
            for (long i = 1; i <= maxN; i++)
            {
                Fact[i] = Fact[i - 1] * i % P;
                InvFact[i] = ModPower(Fact[i], P - 2, P) % P;
            }
        }
    }

    static long ModPower(long x, long n, long mod) // x ^ n
    {
        long res = 1;
        x = (x % mod + mod) % mod;
        while (n > 0)
        {
            if ((n & 1) == 1) res = res * x % mod;
            x = x * x % mod;
            n >>= 1;
        }
        return res;
    }
}

class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    static string[] Split(string s) { return s.Split(separator, op); }
    static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}