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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val mod = 1000000007L
    fun divWithMod(a: Long, b: Long): Long {
        return ((a % mod) * java.math.BigInteger.valueOf(b).modInverse(java.math.BigInteger.valueOf(mod)).toLong()) % mod
    }
    val (h, w, a, b) = readLine()!!.split(' ').map(String::toLong)
    val dataNum = (h + w).toInt()
    val facts = LongArray(dataNum + 1) { 1 }
    (1..dataNum).forEach { facts[it] = (facts[it - 1] * it) % mod }

    var ans = 0L
    for (tw in b + 1..w) {
        val th = h - a
        val m1_1 = facts[(th + tw - 2).toInt()]
        val m1_2 = if (th != 1L) divWithMod(m1_1, facts[th.toInt() - 1]) else m1_1
        val m1_3 = if (tw != 1L) divWithMod(m1_2, facts[tw.toInt() - 1]) else m1_2

        val m2_1 = facts[(a + (w - tw + 1) - 2).toInt()]
        val m2_2 = if (a != 1L) divWithMod(m2_1, facts[a.toInt() - 1]) else m2_1
        val m2_3 = if ((w - tw + 1) != 1L) divWithMod(m2_2, facts[(w - tw + 1).toInt() - 1]) else m2_2

        ans += (m1_3 * m2_3) % mod
        ans %= mod
    }
    println(ans)
}