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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

type i64 int64

const MOD i64 = 1000000007

// n!を保持する配列、n!の逆元を保持する配列
var fact, invf [202020]i64

// b**nをmodで割った余りを返却する
func modPow(b, n, mod i64) i64 {
	if n == 1 {
		return b
	}
    // (b**2)の(n/2)乗として計算
	ret := modPow(b*b%mod, n/2, mod)
	if n&1 == 1 {
		ret = ret * b % mod
	}
	return ret
}

// nの逆元を計算する
func inverse(n i64) i64 {
	return modPow(n, MOD-2, MOD)
}

func comb(n, k i64) i64 {
	if k < 0 || n < k {
		return 0
	}
	return fact[n] * invf[k] % MOD * invf[n-k] % MOD
}

func main() {
	var h, w, a, b, ans i64
	fmt.Scan(&h, &w, &a, &b)

	fact[0] = 1
	invf[0] = 1

	for i := i64(1); i <= 200020; i++ {
		fact[i] = (fact[i-1] * i) % MOD
		invf[i] = inverse(fact[i])
	}

	for i := i64(1); i <= h-a; i++ {
		ans += comb(b-1+i-1, b-1) * comb(w-b-1+h-i, h-i) % MOD
        ans %= MOD
	}
    
    fmt.Println(ans)
}