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.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
using static AtCoder.CalcL;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        //const int MOD = 998244353;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1 };
        static readonly int[] dJ = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var input = cin.ReadSplitInt();
            int H = input[0];
            int W = input[1];
            int A = input[2];
            int B = input[3];
            long ans = 0;
            long prev = 0;
            var md = new Modulo(200010);
            for(var i = 0; i < H - A; i++)
            {
                ans += md.Mul(((md.Ncr(i + B, i) - prev + MOD) % MOD), md.Ncr(W - 1 - B + (H - 1 - i), (H - 1 - i)));
                ans %= MOD;
                prev = md.Ncr(i + B, i);
            }
            Console.WriteLine(ans);

            //Console.Out.Flush();
        }
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
    }
    public class Scanner
    {
        public int[] ReadSplitInt()
        {
            return ConvertAll(Console.ReadLine().Split(), int.Parse);
        }
        public long[] ReadSplitLong()
        {
            return ConvertAll(Console.ReadLine().Split(), long.Parse);
        }
        public double[] ReadSplit_Double()
        {
            return ConvertAll(Console.ReadLine().Split(), double.Parse);
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

        static public long LPow(int a, int b)
        {
            return (long)Pow(a, b);
        }
    }
    static public class CalcI
    {
        public static int Gcd(int a, int b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static int Lcm(int a, int b)
        {
            int g = Gcd(a, b);
            return a / g * b;
        }
        public static int Ceil(int n, int div)
        {
            return (n + div - 1) / div;
        }
    }
    static public class CalcL
    {
        public static long Gcd(long a, long b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static long Lcm(long a, long b)
        {
            long g = Gcd(a, b);
            return a / g * b;
        }
        public static long Ceil(long n, long div)
        {
            return (n + div - 1) / div;
        }
    }
    class Modulo
    {
        private const long M = 1000000007;
        //private const int M = 998244353;
        private readonly long[] m_facs;
        public long Mul(long a, long b)
        {
            return ((a * b) % M);
        }
        public Modulo(long n)
        {
            m_facs = new long[n + 1];
            m_facs[0] = 1;
            for (long i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public long Fac(long n)
        {
            return m_facs[n];
        }
        public long Pow(long a, long m)
        {
            switch (m)
            {
                case 0:
                    return 1L;
                case 1:
                    return a;
                default:
                    long p1 = Pow(a, m / 2);
                    long p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public long Div(long a, long b)
        {
            return Mul(a, Pow(b, M - 2));
        }
        public long Ncr(long n, long r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
        public Modulo() { }
    }
}