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! debug {
    ($($arg:tt)*) => (if cfg!(debug_assertions) {print!("[DEBUG] "); println!($($arg)*)});
}

const MOD: i64 = 1e9 as i64 + 7;

pub fn mod_pow(mut x: i64, mut n: i64) -> i64 {
    let mut res = 1i64;
    while n > 0 {
        if n % 2 == 1 {
            res = res * x % MOD;
        }
        x = x * x % MOD;
        n /= 2;
    }
    res
}

pub fn inv(x: i64) -> i64 {
    mod_pow(x, MOD - 2)
}

fn f(x: usize, y: usize, fact: &Vec<i64>) -> i64 {
    fact[x + y] * inv(fact[x]) % MOD * inv(fact[y]) % MOD
}

const N: usize = 200000;

fn main() {
    let mut rd = reader::Reader::new();

    let mut fact: Vec<i64> = vec![0; N];
    fact[0] = 1;
    for i in 1..N {
        fact[i] = fact[i - 1] * i as i64 % MOD;
    }

    let h: usize = rd.next();
    let w: usize = rd.next();
    let a: usize = rd.next();
    let b: usize = rd.next();

    let mut ans = 0;
    for i in 0..w - b {
        let f1 = f(h - a - 1, b + i, &fact);
        let f2 = f(a - 1, w - b - 1 - i, &fact);
        ans += f1 * f2;
        ans %= MOD;
    }
    print!("{}", ans);
}

mod reader {
    use std::fmt::Debug;
    use std::str::FromStr;
    use std::collections::VecDeque;
    use std::io::{self, Read};

    fn _read_line() -> String {
        let mut buf = String::new();
        let _ = io::stdin().read_to_string(&mut buf);
        buf
    }

    fn _read_vec_deque_string() -> VecDeque<String> {
        _read_line()
            .split_whitespace()
            .map(|s| s.to_string())
            .collect()
    }

    #[allow(dead_code)]
    pub struct Reader {
        buf: VecDeque<String>,
    }

    #[allow(dead_code)]
    impl Reader {
        pub fn new() -> Reader {
            Reader { buf: VecDeque::new() }
        }

        fn update_buf(&mut self) {
            if self.buf.is_empty() {
                self.buf = _read_vec_deque_string();
            }
        }

        pub fn next<T>(&mut self) -> T
            where
                T: FromStr,
                T::Err: Debug,
        {
            self.update_buf();
            self.buf.pop_front().unwrap().parse::<T>().unwrap()
        }

        pub fn next_n<T>(&mut self, n: usize) -> Vec<T>
            where
                T: FromStr,
                T::Err: Debug,
        {
            let mut vec: Vec<T> = Vec::with_capacity(n);

            for _ in 0..n {
                vec.push(self.next());
            }
            vec
        }
    }
}