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(arg: Array<String>) {
    val (H, W, A, B) =  listOfInt()
    var ans = ModInt(0)
    for (h in 1 .. H - A) {
        if (B == W - 1 && h != H - A) continue
        ans += comb(h - 1 + B, B) *
            comb(H - h + W - B - if (h != H - A) 2 else 1, H - h)
    }
    println(ans)
}

var fac = mutableListOf<ModInt>()
private fun fact(n: Int): ModInt {
    if (fac.size == 0) fac.add(ModInt(1))
    while (fac.size <= n) {
        fac.add(fac.last() * ModInt(fac.size))
    }
    return fac[n]
}
private fun comb(n: Int, k: Int) = fact(n) / fact(k) / fact(n - k)


data class ModInt(private var v: Long) {
    companion object { private const val MOD = 1000000007L }
    init { this.v %= MOD }
    constructor(n: Int): this(n.toLong())
    operator fun plus(other: Int) = ModInt((this.v + other) % MOD)
    operator fun plus(other: ModInt) = ModInt((this.v + other.v) % MOD)
    operator fun minus(other: Int) = ModInt((this.v + MOD - other) % MOD)
    operator fun minus(other: ModInt) = ModInt((this.v + MOD - other.v) % MOD)
    operator fun times(other: Int) = ModInt(this.v * other % MOD)
    operator fun times(other: ModInt) = ModInt(this.v * other.v % MOD)
    operator fun div(other: ModInt) = ModInt(this.v * pow(other.v, MOD - 2) % MOD)
    private fun pow(a: Long, b: Long): Long {
        if (b == 0L) return 1L
        if (b % 2 == 0L) {
            val d = pow(a, b / 2)
            return (d * d) % MOD
        }
        return a * pow(a, b - 1) % MOD
    }
    override fun toString() = this.v.toString()
}

fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfLong() = listOfString().map(String::toLong)
fun listOfInt(delta: Int = 0) = listOfString().map { Integer.parseInt(it) + delta }

//10000