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.Text;
using System.Threading.Tasks;

namespace ConsoleApp96 {
    class Program {
        static long mod = 1000000007;

        static long[] factorialMod;
        static long[] factorialModInv;

        static void Main(string[] args) {
            var st = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long H = st[0];
            long W = st[1];
            long A = st[2];
            long B = st[3];

            long ans = 0;

            factorialMod = new long[200010];
            factorialModInv = new long[200010];

            for (int i = 0; i < 200000; i++) {
                if (i <= 1) {
                    factorialMod[i] = 1;
                    continue;
                }

                factorialMod[i] = i * factorialMod[i - 1] % mod;
            }

            for (int i = 0; i < 200000; i++) {
                if (i <= 1) {
                    factorialModInv[i] = 1;
                    continue;
                }

                factorialModInv[i] = ModInv(i) * factorialModInv[i - 1] % mod;
            }


            for (long i = 0; B + i < W; i++) {
                //Console.WriteLine(i);
                //Console.WriteLine(CalculateCMod(H - A, B + i + 1));
                //Console.WriteLine(CalculateCMod(A, W - B - i));

                ans += CalculateCMod(H - A, B + i + 1) % mod * CalculateCMod(A, W - B - i) % mod;
                ans %= mod;
            }
            Console.WriteLine(ans % mod);
        }

        //aマス×bマスの行き方の合計のmod
        static long CalculateCMod(long a, long b) {
            return factorialMod[a + b - 2] % mod * (factorialModInv[a - 1]) % mod * (factorialModInv[b - 1]) % mod;

            //return FactoricalMod(a + b - 2) % mod * (FactoricalModInv(a - 1)) % mod * (FactoricalModInv(b - 1)) % mod;
        }

        static long FactoricalMod(long a) {
            if (a <= 1) {
                return 1;
            }
            return a * FactoricalMod(a - 1) % mod;
        }

        static long ModInv(long a) {
            if (a <= 1) {
                return 1;
            }

            long ret = -(ModInv(mod % a) * (mod / a)) % mod;
            if (ret < 0) {
                ret += mod;
            }
            return ret;
        }

        static long FactoricalModInv(long a) {
            if (a <= 1) {
                return 1;
            }

            return ModInv(a) * FactoricalModInv(a - 1) % mod;
        }
    }
}