#[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;
mod util {
    use std::fmt::Debug;
    use std::io::{stdin, stdout, BufWriter, StdoutLock};
    use std::str::FromStr;
    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }
    #[allow(dead_code)]
    pub fn chars() -> Vec<char> {
        line().chars().collect()
    }
    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }
    #[allow(dead_code)]
    pub fn with_bufwriter<F: FnOnce(BufWriter<StdoutLock>) -> ()>(f: F) {
        let out = stdout();
        let writer = BufWriter::new(out.lock());
        f(writer)
    }
}
#[allow(unused_macros)]
macro_rules ! get { ( [ $ t : ty ] ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . split_whitespace ( ) . map ( | t | t . parse ::<$ t > ( ) . unwrap ( ) ) . collect ::< Vec < _ >> ( ) } } ; ( [ $ t : ty ] ; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( [ $ t ] ) ) . collect ::< Vec < _ >> ( ) } ; ( $ t : ty ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . trim ( ) . parse ::<$ t > ( ) . unwrap ( ) } } ; ( $ ( $ t : ty ) ,* ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; let mut iter = line . split_whitespace ( ) ; ( $ ( iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) , ) * ) } } ; ( $ t : ty ; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ ( $ t : ty ) ,*; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ ( $ t ) ,* ) ) . collect ::< Vec < _ >> ( ) } ; }
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
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();
    }
}

#[allow(dead_code)]
pub const M: u64 = 1_000_000_007;

fn solve() {
    let (n, m) = get!(usize, usize);
    let a = get!([usize]);
    let b = get!([usize]);

    let a_set: HashSet<usize> = a.into_iter().collect();
    let b_set: HashSet<usize> = b.into_iter().collect();

    let mut ans = 1;
    let mut x = 0;
    let mut y = 0;
    let mut k = 0;

    for i in 0..n * m {
        if ans == 0 {
            break;
        }

        let v = (n * m) - i;

        match (a_set.contains(&v), b_set.contains(&v)) {
            (true, true) => {
                x += 1;
                y += 1;
                k += 1;
            }
            (true, false) => {
                ans *= y as u64;
                x += 1;
                k += 1;
            }
            (false, true) => {
                ans *= x as u64;
                y += 1;
                k += 1;
            }
            (false, false) => {
                ans *= (x * y - k) as u64;
                k += 1;
            }
        }

        ans %= M;
    }

    println!("{}", ans);
}


Measured memory_bytes: 8572