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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Tasks
{
    public class D
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var HWAB = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
            var (H, W, A, B) = (HWAB[0], HWAB[1], HWAB[2], HWAB[3]);
            var p = (long)1e9 + 7;
            var answer = 0L;
            for (var i = 0; i < H - A; i++)
            {
                var way1 = Enumeration.CombinationCount(i + B - 1, B - 1, p);
                var way2 = Enumeration.CombinationCount(H - i - 1 + W - B - 1, W - B - 1, p);
                answer += (way1 * way2) % p;
                answer %= p;
            }
            Console.WriteLine(answer);
        }

        public static class Enumeration
        {
            private static Dictionary<long, long> _memo = new Dictionary<long, long> { { 0, 1 }, { 1, 1 } };
            private static Dictionary<long, long> _modMemo = new Dictionary<long, long> { { 0, 1 }, { 1, 1 } };
            private static long _max = 1;
            private static long _modMax = 1;

            public static long Fractorial(long n)
            {
                if (_memo.ContainsKey(n)) return _memo[n];
                if (n < 0) throw new ArgumentException();
                var val = _memo[_max];
                for (var i = _max + 1; i <= n; i++)
                {
                    val *= i;
                    _memo[i] = val;
                }
                _max = n;
                return _memo[n];
            }

            public static long Fractorial(long n, long mod)
            {
                if (_modMemo.ContainsKey(n)) return _modMemo[n];
                if (n < 0) throw new ArgumentException();
                var val = _modMemo[_modMax];
                for (var i = _modMax + 1; i <= n; i++)
                {
                    val *= i % mod;
                    val %= mod;
                    _modMemo[i] = val;
                }
                _modMax = n;
                return _modMemo[n];
            }

            public static long PermutationCount(long n, long k)
            {
                if (n < k) throw new ArgumentException();
                return Fractorial(n) / Fractorial(n - k);
            }

            public static long PermutationCount(long n, long k, long mod)
            {
                if (n < k) throw new ArgumentException();
                var top = Fractorial(n, mod);
                var bottom = Fractorial(n - k, mod);
                return (top * Power(bottom, mod - 2, mod)) % mod;
            }

            public static long CombinationCount(long n, long k)
            {
                if (n < k) throw new ArgumentException();
                return Fractorial(n) / (Fractorial(k) * Fractorial(n - k));
            }

            public static long CombinationCount(long n, long k, long mod)
            {
                if (n < k) throw new ArgumentException();
                var top = Fractorial(n, mod);
                var bottom = (Fractorial(k, mod) * Fractorial(n - k, mod)) % mod;
                return (top * Power(bottom, mod - 2, mod)) % mod;
            }

            public static long Power(long x, long y, long mod)
            {
                var result = 1L;
                while (y > 0)
                {
                    if ((y & 1) == 1) result = ((result % mod) * (x % mod)) % mod;
                    x = ((x % mod) * (x % mod)) % mod;
                    y >>= 1;
                }
                return result;
            }
        }
    }
}