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 Rust (1.15.1) (judge verdict: Runtime Error)

fn main() {
    let (h, w, a, b): (usize, usize, usize, usize) = (read(), read(), read(), read());

    let mut dp: Vec<Vec<i64>> = vec![vec![0;w]; h];
    for i in 0..h {
        for j in 0..w {
            if h-i-1 < a && b > j {
                dp[i][j] = 0;
            } else if i == 0 || j == 0 {
                dp[i][j] = 1;
            } else if dp[i-1][j] != 0 && dp[i][j-1] != 0 {
                dp[i][j] = (dp[i-1][j] + dp[i][j-1]) % MOD;
            } else {
                dp[i][j] = dp[i-1][j];
            }
        }
    }
    let ans = dp[h-1][w-1];
    println!("{}", ans);
}


// 以下関数

use std::io::*;
use std::str::FromStr;
pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

pub const MOD: i64 = 1_000_000_007;

pub fn is_prime(n: i32) -> bool {
    if n < 2 {
        return false;
    } else if n == 2 {
        return true;
    }
    let mut i = 2;
    while i * i < n {
        if n % i == 0 {
            return false;
        } else {
            i += 1;
            continue;
        }
    }
    true
}

pub fn lcm(mut n: i32, mut m: i32) -> i32 {
    n = if n > m { m } else { n };
    m = if n > m { n } else { m };
    let mut i = n;
    while i % m != 0 {
        i += n;
    }
    i
}

pub fn abs(n: i32) -> i32 {
    if n >= 0 {
        n
    } else {
        -n
    }
}

pub fn max<T: PartialOrd>(n: T, m: T) -> T {
    if n >= m {
        n
    } else {
        m
    }
}

pub fn min<T: PartialOrd>(n: T, m: T) -> T {
    if n <= m {
        n
    } else {
        m
    }
}

pub fn factorial(n: u32) -> u32 {
    if n == 0 {
        return 1;
    }
    let mut r = n;
    for i in 0..n - 1 {
        r *= n - i - 1;
    }
    r
}

pub fn combination(n: u32, m: u32) -> u32 {
    factorial(n) / factorial(m) / factorial(n - m)
}