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::BufRead;

const P: u64 = 1_000_000_007;

fn main() {
    let stdin = std::io::stdin();
    let val = stdin.lock().gets().split(' ')
        .map(|x| x.parse().unwrap()).collect::<Vec<u64>>();
    let (h, w, a, b) = (val[0], val[1], val[2], val[3]);
    let bc = BinomialCoefModP::new(h - 1 + w - 1, P);
    let mut ans = 0;
    for i in 0..std::cmp::min(h - a, w - b) {
        let (px, py) = (b + 1 + i, h - a - i);
        ans += bc.get(px - 1 + py - 1, py - 1) *
            bc.get(w - px + h - py, h - py) % P;
    }
    println!("{}", ans % P);
}

trait Gets { fn gets(&mut self) -> String; }
impl<T: std::io::BufRead> Gets for T {
    fn gets(&mut self) -> String { self.lines().next().unwrap().unwrap() } }

struct BinomialCoefModP {
    num: Vec<u64>,
    denom: Vec<u64>,
    p: u64,
}

impl BinomialCoefModP {
    fn new(max_n: u64, p: u64) -> BinomialCoefModP {
        let mut num = Vec::with_capacity(max_n as usize + 1);
        num.push(1);
        for i in 0..max_n {
            let tmp = num[i as usize] * (i + 1) % p;
            num.push(tmp);
        }
        let denom = num.iter().map(|&x| Self::inv(x, p)).collect();
        BinomialCoefModP { num: num, denom: denom, p: p }
    }

    fn get(&self, n: u64, k: u64) -> u64 {
        let (n, k) = (n as usize, k as usize);
        self.num[n] * self.denom[n - k] % self.p * self.denom[k] % self.p
    }

    fn inv(mut n: u64, p: u64) -> u64 {
        let mut x = p - 2;
        let mut inv = 1;
        while x != 0 {
            if x & 1 != 0 {
                inv = inv * n % p;
            }
            x >>= 1;
            n = n * n % p;
        }
        inv
    }
}