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 (1.42.0) (judge verdict: Accepted)

#![allow(dead_code,unused_variables)]
use proconio::{fastout, input};
const MOD: usize = 1_000_000_007;

#[fastout]
fn main() {
    input! {
        h: usize,
        w: usize,
        a: usize,
        b: usize,
    }

    let mut ans = 0;
    let c = Combination::new(h+w,MOD);
    for i in 0..(h-a){
        // println!("{} {}",h+w-i-b,w-b);
        let res = c.comb(i+b-1, i) * c.comb(h+w-b-i-2, w-b-1);
        // println!("{} {}",c.comb(i+1+b-1, b-1) , c.comb(h-i+w-b-1, w-b));
        ans = (ans + res) % MOD;
    }

    println!("{}",ans);

}

pub struct Combination{
    fac : Vec<usize>,
    finv : Vec<usize>,
    m : usize,
}

impl Combination{
    pub fn new(n : usize, m : usize) -> Self{
        let mut inv = vec![1;n+1];
        let mut fac = vec![1;n+1];
        let mut finv = vec![1;n+1];

        for i in 2..(n+1){
            fac[i] = (fac[i-1] * i) % m;
            inv[i] = m - (inv[m%i] * (m/i) % m);
            finv[i] = (finv[i-1]*inv[i])%m;
        }

        Combination{
            fac,
            finv,
            m,
        }
    }

    pub fn comb(&self, n : usize, k: usize) -> usize{
        if n < k{
            return 0;
        }

        (self.fac[n] * (self.finv[k] * self.finv[n-k] % self.m)) % self.m
    }
}