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)

#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}
impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}
impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                if len == 0 {
                    break;
                }
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    input!{
        H:usize,W:usize,A:usize,B:usize,
    }
    let p = 1_000_000_007;
    let modcomb = ModComb::new(300001,p);
    let mut res=0;
    for i in 1..(H-A+1) {
        let choice0_i=i-1;
        let choice0_j=B-1;

        let choice1_i=H-(i-1)-1;
        let choice1_j=W-B-1;
        // dbg!(choice0_i,choice0_j,choice1_i,choice1_j);

        let mut c0 = modcomb.nCk(choice0_i+choice0_j,choice0_i);
        let mut c1 = modcomb.nCk(choice1_i+choice1_j,choice1_i);
        res += (c0*c1)%p;
        res %= p;
    }
    println!("{}",res);
}
#[allow(dead_code)]
#[doc = " x ^ n % m"]
pub fn modpow(x: usize, n: usize, m: usize) -> usize {
    let mut res = 1;
    let mut x = x % m;
    let mut n = n;
    while n > 0 {
        if n & 1 == 1 {
            res = (res * x) % m;
        }
        x = (x * x) % m;
        n >>= 1;
    }
    res
}
struct ModComb {
    fact: Vec<usize>,
    fact_inv: Vec<usize>,
    n: usize,
    p: usize,
}
impl ModComb {
    fn initialize(ft: &mut Self) {
        let n = ft.n as usize;
        ft.fact[0] = 1;
        for i in 1..n {
            ft.fact[i] = (ft.fact[i - 1] * i) % ft.p;
        }
        ft.fact_inv[n - 1] = modpow(ft.fact[n - 1], ft.p - 2, ft.p);
        for i in (0..n - 1).rev() {
            ft.fact_inv[i] = (ft.fact_inv[i + 1] * (i + 1)) % ft.p;
        }
    }
    fn new(max_n: usize, p: usize) -> ModComb {
        let mut ft = ModComb {
            fact: vec![0; max_n + 1 as usize],
            fact_inv: vec![0; max_n + 1 as usize],
            n: max_n + 1,
            p: p,
        };
        Self::initialize(&mut ft);
        ft
    }
    fn fact(&self, n: usize) -> usize {
        self.fact[n]
    }
    fn nCk(&self, n: usize, k: usize) -> usize {
        if n < k {
            return 0;
        }
        (self.nPk(n, k) * self.fact_inv[k]) % self.p
    }
    fn nPk(&self, n: usize, k: usize) -> usize {
        if n < k {
            return 0;
        }
        self.fact[n] * self.fact_inv[n - k] % self.p
    }
    fn nHk(&self, n: usize, k: usize) -> usize {
        if n == 0 && k == 0 {
            return 1;
        }
        self.nCk(n + k - 1, k)
    }
    fn nSk(&self, n: usize, k: usize) -> usize {
        if n < k {
            return 0;
        }
        let mut res = 0;
        for i in 0..k + 1 {
            let v = self.nCk(k, i) * modpow(i, n, self.p) % self.p;
            if (k - i) % 2 == 1 {
                res = (res + self.p - v) % self.p;
            } else {
                res = (res + v) % self.p;
            }
        }
        return res * self.fact_inv[k] % self.p;
    }
    fn nBk(&self, n: usize, k: usize) -> usize {
        0
    }
}