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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace D
{
    class Program
    {
        const long M = 1000000007;
        static long Mul(long s, long e)
        {
            var ans = 1L;
            for (long now = s; now <= e; now++)
            {
                ans *= now;
                ans %= M;
            }
            return ans;
        }

        static long Pow(long b, long e)
        {
            if (e == 0) { return 1; }
            else if (e % 2 == 0) { return Pow((b * b) % M, e / 2); }
            else
            {
                return (b * Pow(b * b % M, (e - 1) / 2)) % M;
            }
        }

        static long Reciprocal(long x)
        {
            return Pow(x, M - 2);
        }
        static long Combination(long n, long r)
        {
            //var numerator = Mul(n - r + 1, n);
            //var denominator = Mul(1, r);
            //return numerator * Reciprocal(denominator) % M;
            return factTable[n] * factRTable[n - r] % M * factRTable[r] % M;
        }

        static long[] factTable;
        static long[] factRTable;

        static void initTable(long max)
        {
            factTable = new long[max];
            factRTable = new long[max];
            long a = 1;
            factTable[0] = factRTable[0] = 1;
            for (int i = 1; i < max; i++)
            {
                a = a * i % M;
                factTable[i] = a;
                factRTable[i] = Reciprocal(a);
            }
        }
        static void Main(string[] args)
        {
            var buff = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            long H = buff[0], W = buff[1], A = buff[2], B = buff[3];

            var a = new long[2, W - B];
            initTable(H + W);
            for (int i = 0; i < W - B; i++)
            {
                a[0, i] = Combination(H - A - 1 + B + i, H - A - 1);
            }
            var now = 0;
            for (int i = 0; i < A; i++)
            {
                a[now ^ 1, 0] = a[now, 0];
                for (int j = 1; j < W - B; j++)
                {
                    a[now ^ 1, j] = (a[now, j] + a[now ^ 1, j - 1]) % M;
                }
                now ^= 1;
            }
            Console.WriteLine(a[now, W - B - 1]);
        }
    }
}