use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;
use std::iter::FromIterator;

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());
    let n = scan.read::<usize>();
    let m = scan.read::<usize>();
    let mut a = scan.readn::<usize>(n);
    let mut b = scan.readn::<usize>(m);
    a.sort();
    b.sort();
    let acnt = a.iter().cloned().collect::<Counter<_>>();
    let bcnt = b.iter().cloned().collect::<Counter<_>>();
    if acnt.values().any(|x| *x >= 2) || bcnt.values().any(|x| *x >= 2) {
        println!("{}", 0);
        return;
    }
    let mut ret = Co(1);
    for i in (1..n * m + 1).rev() {
        if acnt.contains_key(&i) && bcnt.contains_key(&i) {
        } else if acnt.contains_key(&i) {
            let p = m - lower_bound(&b, &i);
            ret *= p.into();
        } else if bcnt.contains_key(&i) {
            let p = n - lower_bound(&a, &i);
            ret *= p.into();
        } else {
            let q = n - lower_bound(&a, &i);
            let p = m - lower_bound(&b, &i);
            ret *= Co(q as i64) * p.into() - (n * m - i).into();
        }
    }
    println!("{}", ret);
}

#[allow(dead_code)]
fn lower_bound<T: Ord>(arr: &[T], x: &T) -> usize {
    let mut ok = arr.len() as i64;
    let mut ng = -1i64;
    while (ok - ng).abs() > 1 {
        let mid = (ok + ng) / 2;
        if &arr[mid as usize] >= x {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    ok as usize
}

#[allow(dead_code)]
fn upper_bound<T: Ord>(arr: &[T], x: &T) -> usize {
    let mut ok = arr.len() as i64;
    let mut ng = -1i64;
    while (ok - ng).abs() > 1 {
        let mid = (ok + ng) / 2;
        if &arr[mid as usize] > x {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    ok as usize
}


// region counter

use std::collections::HashMap;
use std::hash::Hash;
use std::ops::*;

#[derive(Clone, Debug)]
struct Counter<K: Eq + Hash> {
    cnt: HashMap<K, i64>,
    d: i64,
}

#[allow(dead_code)]
impl <K: Eq + Hash> Counter<K> {
    fn new() -> Counter<K> {
        Counter {cnt: HashMap::new(), d: 0}
    }
}

#[allow(dead_code)]
impl <K: Eq + Hash> Deref for Counter<K> {
    type Target = HashMap<K, i64>;
    fn deref(&self) -> &Self::Target {
        &self.cnt
    }
}

#[allow(dead_code)]
impl <K: Eq + Hash> DerefMut for Counter<K> {
    fn deref_mut(&mut self) -> &mut Self::Target {
        &mut self.cnt
    }
}

#[allow(dead_code)]
impl<K: Eq + Hash> Index<K> for Counter<K> {
    type Output = i64;

    fn index(&self, index: K) -> &Self::Output {
        self.cnt.get(&index).unwrap_or(&self.d)
    }
}

#[allow(dead_code)]
impl<K: Eq + Hash + Clone> IndexMut<K> for Counter<K> {
    fn index_mut(&mut self, index: K) -> &mut i64 {
        if !self.cnt.contains_key(&index) {
            self.cnt.insert(index.clone(), self.d);
        }
        self.cnt.get_mut(&index).unwrap()
    }
}

#[allow(dead_code)]
impl<K: Eq + Hash> std::iter::FromIterator<K> for Counter<K> {
    fn from_iter<T: IntoIterator<Item=K>>(iter: T) -> Self {
        let mut cnt = HashMap::new();
        for i in iter {
            *cnt.entry(i).or_insert(0) += 1;
        }
        Counter {cnt: cnt, d: 0}
    }
}
// endregion

#[allow(dead_code)]
const M: i64 = 1_000_000_007;

// region modulo
#[allow(dead_code)]
use std::ops::*;

#[allow(dead_code)]
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct Co (pub i64);

#[allow(dead_code)]
impl Co {
    pub fn pow(self, mut n: i64) -> Self {
        let mut a = self;
        let mut res = Co(1);
        while n > 0 {
            if n & 1 == 1 {
                res *= a;
            }
            a = a * a;
            n >>= 1;
        }
        res
    }
}

#[allow(dead_code)]
impl std::fmt::Display for Co {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

#[allow(dead_code)]
impl From<i32> for Co {
    fn from(value: i32) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl From<i64> for Co {
    fn from(value: i64) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl From<usize> for Co {
    fn from(value: usize) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl AddAssign for Co {
    fn add_assign(&mut self, other: Self) {
        *self = self.add(other);
    }
}
#[allow(dead_code)]
impl Add for Co {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        Co::from((self.0).add(other.0))
    }
}
#[allow(dead_code)]
impl SubAssign for Co {
    fn sub_assign(&mut self, other: Self) {
        *self = self.sub(other);
    }
}
#[allow(dead_code)]
impl Sub for Co {
    type Output = Self;
    fn sub(self, other: Self) -> Self {
        Co::from((self.0).sub(other.0))
    }
}
#[allow(dead_code)]
impl MulAssign for Co {
    fn mul_assign(&mut self, other: Self) {
        *self = self.mul(other);
    }
}
#[allow(dead_code)]
impl Mul for Co {
    type Output = Self;
    fn mul(self, other: Self) -> Self {
        Co::from((self.0).mul(other.0))
    }
}
#[allow(dead_code)]
impl DivAssign for Co {
    fn div_assign(&mut self, other: Self) {
        *self = self.div(other);
    }
}
#[allow(dead_code)]
impl Div for Co {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        self * rhs.pow((M - 2) as i64)
    }
}
// endregion

// region template
#[allow(dead_code)]
fn iu(i: i64) -> usize { i as usize }

#[allow(dead_code)]
fn ui(i: usize) -> i64 { i as i64 }

#[allow(dead_code, deprecated)]
fn join<T: std::fmt::Display>(slice: &[T], sep: &str) -> String {
    let strings = slice.iter().map(|t| format!("{}", t)).collect::<Vec<_>>();
    strings.connect(sep)
}

#[allow(dead_code)]
fn arr<'a, S, T>(n: usize, mut f: S) -> Vec<T> where S: FnMut(usize) -> T + 'a {
    (0..n).map(|i| f(i)).collect::<Vec<T>>()
}

#[allow(dead_code)]
fn alt<S, T>(v: Vec<S>) -> T where T: FromIterator<S> {
    v.into_iter().collect::<T>()
}

#[allow(dead_code)]
fn dup<S, T>(v: &[S]) -> T where T: FromIterator<S>, S: Clone {
    v.iter().cloned().collect::<T>()
}

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect()
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion

Measured memory_bytes: 4352