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: Accepted)

#[allow(unused_macros)]
macro_rules! input_byline {
    ($($r:tt)* ) => {
        let stdin = std::io::stdin();
        let mut q = std::collections::VecDeque::new();
        let mut next = || {
            if q.is_empty() {
                let mut s = String::new();
                stdin.read_line(&mut s);
                for v in s.split_whitespace() {
                    q.push_back(v.to_string());
                }
            }
            q.pop_front().unwrap()
        };
        input_inner!{next, $($r)*}
    };

}

#[allow(unused_macros)]
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

trait Printable {
    fn p(&self);
}

impl<T: std::fmt::Display> Printable for T {
    fn p(&self) {
        println!("{}", self);
    }
}

impl<T: std::fmt::Display> Printable for [T] {
    fn p(&self) {
        for i in 0..self.len() {
            if i != 0 {
                print!(" ");
            }
            print!("{}", self[i]);
        }
        println!("");
    }
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;

struct Combination {
    modp: usize,
    mfact: Vec<usize>,
    rfact: Vec<usize>,
}

impl Combination {
    fn new(size: usize, modp: usize) -> Self {
        let mut rfact = vec![0; size + 1];
        let mut mfact = vec![0; size + 1];
        mfact[0] = 1;
        for i in 1..mfact.len() {
            mfact[i] = (mfact[i - 1] * i) % modp;
        }
        rfact[size] = Self::inv(mfact[size], modp);
        for i in (0..size).rev() {
            rfact[i] = rfact[i + 1] * (i + 1) % modp;
        }

        Combination {
            modp: modp,
            mfact: mfact,
            rfact: rfact,
        }
    }

    fn pow(mut x: usize, mut n: usize, modp: usize) -> usize {
        let mut ret = 1;
        while n > 0 {
            if n & 1 > 0 {
                ret *= x;
                ret %= modp;
            }
            x *= x;
            x %= modp;
            n >>= 1;
        }
        ret
    }

    fn inv(x: usize, modp: usize) -> usize {
        Self::pow(x, modp - 2, modp)
    }

    fn C(&self, p: usize, q: usize) -> usize {
        if p < q {
            return 0;
        }
        (((self.mfact[p] * self.rfact[q]) % self.modp) * self.rfact[p - q]) % self.modp
    }
}

const M: usize = 1e9 as usize + 7;

fn main() {
    input! {
        h: usize,
        w: usize,
        a: usize,
        b: usize,
    }

    let mut sum = 0;
    let comb = Combination::new(200001, M);
    for i in 0..h - a {
        let mut s = comb.C(i + b - 1, b - 1) * comb.C(h - i - 1 + w - b - 1, h - i - 1);
        s %= M;
        sum += s;
        sum %= M;
    }

    println!("{}", sum);
}