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)

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;
use std::iter::FromIterator;

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());
    let comb = Comb::new(200_001);
    let h = scan.read::<usize>();
    let w = scan.read::<usize>();
    let a = scan.read::<usize>();
    let b = scan.read::<usize>();
    let mut ret = 0;
    for p in 0..h - a {
        let left = comb.of(b-1+p, b-1);
        let right = comb.of(h-p-1+w-1-b, h-p-1);
        ret += (left * right) % M;
        ret %= M;
    }
    println!("{}", ret);
}

#[allow(dead_code)]
const M: i64 = 1_000_000_007;

#[allow(dead_code)]
struct Comb {
    fac: Vec<i64>,
    finv: Vec<i64>,
    inv: Vec<i64>
}

#[allow(dead_code)]
impl Comb {
    fn new(n: usize) -> Self {
        let mut fac = vec![0;n];
        let mut finv = vec![0;n];
        let mut inv = vec![0;n];
        fac[0] = 1;
        fac[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;
        for i in 2..n {
            let i_i64 = i as i64;
            fac[i] = fac[i-1] * i_i64 % M;
            inv[i] = M - inv[(M%i_i64) as usize] * (M / i_i64) % M;
            finv[i] = finv[i-1] * inv[i] % M;
        }
        Comb {
            fac: fac, finv: finv, inv: inv
        }
    }
    fn of(&self, n: usize, k: usize) -> i64 {
        if n < k {0}
        else {self.fac[n] * (self.finv[k] * self.finv[n - k] % M) % M}
    }
    /// combination with repetition
    fn rep(&self, n: usize, k: usize) -> i64 {
        self.of(n + k - 1, k)
    }
    fn perm(&self, n: usize, k: usize) -> i64 {
        if n < k {0}
        else {self.fac[n] * self.finv[n-k] % M}
    }
}

// region template
#[allow(dead_code)]
fn iu(i: isize) -> usize { i as usize }

#[allow(dead_code)]
fn ui(i: usize) -> isize { i as isize }

#[allow(dead_code, deprecated)]
fn join<T: std::fmt::Display>(slice: &[T], sep: &str) -> String {
    let strings = slice.iter().map(|t| format!("{}", t)).collect::<Vec<_>>();
    strings.connect(sep)
}

#[allow(dead_code)]
fn arr<'a, S, T>(n: usize, mut f: S) -> Vec<T> where S: FnMut(usize) -> T + 'a {
    (0..n).map(|i| f(i)).collect::<Vec<T>>()
}

#[allow(dead_code)]
fn alt<S, T>(v: Vec<S>) -> T where T: FromIterator<S> {
    v.into_iter().collect::<T>()
}

#[allow(dead_code)]
fn dup<S, T>(v: &[S]) -> T where T: FromIterator<S>, S: Clone {
    v.iter().cloned().collect::<T>()
}

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect()
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion