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.Linq;

namespace AtCoder.ABC042
{
    class ProblemD
    {
        private static readonly long Mod = 1000000007;
        static long[] FactCache;
        static long[] InverseFactCache;
        static void Main()
        {
            FactCache = new long[100000 * 2];
            FactCache[0] = 1;
            for (var i = 1; i < FactCache.Length; i++)
            {
                FactCache[i] = FactCache[i - 1] * i % Mod;
            }

            InverseFactCache = new long[100000];
            InverseFactCache[0] = 1;
            for (var i = 1; i < InverseFactCache.Length; i++)
            {
                InverseFactCache[i] = InverseFactCache[i - 1] * InverseMod(i, Mod) % Mod;
            }

            var values = ReadIntArray();
            //var values = new[] { 100000, 100000, 44444, 55555 };
            var h = values[0];
            var w = values[1];
            var a = values[2];
            var b = values[3];
            long answer = 0;
            for (long i = 0; i < h - a; i++)
            {
                answer += GetPattern(b - 1, i) * GetPattern(w - b - 1, h - i - 1) % Mod;
                answer %= Mod;
            }
            Console.WriteLine($"{answer % Mod}");
        }

        static long ExtGcd(long a, long b, ref long x, ref long y)
        {
            if (b == 0)
            {
                x = 1;
                y = 0;
                return a;
            }
            var q = a / b;
            var g = ExtGcd(b, a - q * b, ref x, ref y);
            var z = x - q * y;
            x = y;
            y = z;
            return g;
        }
        static long InverseMod(long a, long m)
        {
            long x = 0;
            long y = 0;
            ExtGcd(a, m, ref x, ref y);
            x %= m;
            if (x < 0) x += m;
            return x;

        }

        static long GetPattern(long x, long y)
        {
            return FactCache[x + y] * InverseFactCache[x] % Mod * InverseFactCache[y] % Mod;
        }

        static long Fraction(long x)
        {
            return FactCache[x];
        }

        public static string ReadLine() => Console.ReadLine();

        public static int ReadInt() => int.Parse(ReadLine());

        public static int[] ReadIntArray() => ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
    }
}