#[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;
#[macro_export]
macro_rules ! chmax { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: max ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! chmin { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: min ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! max { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: max ( $ x , max ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! min { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: min ( $ x , min ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! dvec { ( $ t : expr ; $ len : expr ) => { vec ! [ $ t ; $ len ] } ; ( $ t : expr ; $ len : expr , $ ( $ rest : expr ) ,* ) => { vec ! [ dvec ! ( $ t ; $ ( $ rest ) ,* ) ; $ len ] } ; }
#[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() {
    let out = stdout();
    let mut out = BufWriter::new(out.lock());

    input!{
        n:usize,m:usize,
        a:[usize;n],
        b:[usize;m],
    }



    let mut a = a;
    let mut b = b;
    a.sort();
    b.sort();

    let mut ok = true;
    let ra = run_length_compression(&a);
    let rb = run_length_compression(&b);
    for x in ra {
        if x.1 >= 2 {
            ok = false;
        }
    }
    for x in rb {
        if x.1 >= 2 {
            ok = false;
        }
    }
    if !ok {
        println!("0");
        return
    }

    let mut acum = CumSum1::new(n*m+1);
    let mut bcum = CumSum1::new(n*m+1);
    for i in 0..n {
        acum.set(a[i], 1);
    }
    acum.build();
    for i in 0..m {
        bcum.set(b[i], 1);
    }
    bcum.build();

    let mut cnt: Mod = 1.into();
    for x in 1..(n*m+1) {
        let ahas = acum.query(x, x+1) == 1;
        let bhas = bcum.query(x, x+1) == 1;
        if ahas && bhas {
            cnt *= 1;
        } else if !ahas && !bhas {
            let mut tmp = acum.query(x, n*m+1) * bcum.query(x, n*m+1);
            tmp -= (n*m-x) as i64;
            cnt *= tmp;
        } else if ahas {
            cnt *= bcum.query(x, n*m+1);
        } else if bhas {
            cnt *= acum.query(x, n*m+1);
        } else {
            unreachable!();
        }
    }
    println!("{}", cnt);
}

#[doc = "O(N)"]
fn run_length_compression<T: Eq + Clone>(xs: &[T]) -> Vec<(T, usize)> {
    if xs.is_empty() {
        return vec![];
    }
    let mut cur = &xs[0];
    let mut rep = 1;
    let mut res = vec![];
    for i in 1..xs.len() {
        if &xs[i] == cur {
            rep += 1;
        } else {
            res.push((cur.clone(), rep));
            cur = &xs[i];
            rep = 1
        }
    }
    res.push((cur.clone(), rep));
    res
}

struct CumSum1 {
    base: Vec<i64>,
    dp: Vec<i64>,
}
impl CumSum1 {
    fn new(n: usize) -> CumSum1 {
        CumSum1 {
            base: vec![0; n],
            dp: vec![],
        }
    }
    fn add(&mut self, i: usize, x: i64) {
        self.base[i] += x;
    }
    fn set(&mut self, i: usize, x: i64) {
        self.base[i] = x;
    }
    fn build(&mut self) {
        let n = self.base.len();
        let mut dp = vec![0; n + 1];
        let mut acc = 0;
        for i in 0..n {
            acc += self.base[i];
            dp[i + 1] = acc;
        }
        self.dp = dp;
    }
    #[doc = "[i,j)"]
    fn query(&self, i: usize, j: usize) -> i64 {
        self.dp[j] - self.dp[i]
    }
}

pub mod modular {
    const M: i64 = 1_000_000_007;
    #[derive(Debug, Clone, Copy, Default, PartialOrd, Ord, PartialEq, Eq)]
    pub struct Mod(i64);
    impl ::std::fmt::Display for Mod {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
    impl Mod {
        pub fn new(v: i64) -> Mod {
            Mod(v % M)
        }
        pub fn pow(self, mut r: i64) -> Mod {
            let mut k = self;
            let mut ret = 1.into();
            while r > 0 {
                if r % 2 != 0 {
                    ret = ret * k;
                }
                r /= 2;
                k = k * k;
            }
            ret
        }
        pub fn recip(self) -> Mod {
            self.pow(M - 2)
        }
    }
    use std::ops::*;
    impl<T: Into<Mod>> Add<T> for Mod {
        type Output = Mod;
        fn add(self, rhs: T) -> Self::Output {
            Mod::new(self.0 + rhs.into().0)
        }
    }
    impl<T: Into<Mod>> AddAssign<T> for Mod {
        fn add_assign(&mut self, rhs: T) {
            *self = *self + rhs;
        }
    }
    impl<T: Into<Mod>> Sub<T> for Mod {
        type Output = Mod;
        fn sub(self, rhs: T) -> Self::Output {
            Mod::new(self.0 - rhs.into().0 + M)
        }
    }
    impl<T: Into<Mod>> SubAssign<T> for Mod {
        fn sub_assign(&mut self, rhs: T) {
            *self = *self - rhs;
        }
    }
    impl<T: Into<Mod>> Mul<T> for Mod {
        type Output = Mod;
        fn mul(self, rhs: T) -> Self::Output {
            Mod::new(self.0 * rhs.into().0)
        }
    }
    impl<T: Into<Mod>> MulAssign<T> for Mod {
        fn mul_assign(&mut self, rhs: T) {
            *self = *self * rhs;
        }
    }
    impl<T: Into<Mod>> Div<T> for Mod {
        type Output = Mod;
        fn div(self, rhs: T) -> Self::Output {
            self * rhs.into().recip()
        }
    }
    impl<T: Into<Mod>> DivAssign<T> for Mod {
        fn div_assign(&mut self, rhs: T) {
            *self = *self / rhs;
        }
    }
    impl Neg for Mod {
        type Output = Mod;
        fn neg(self) -> Self::Output {
            Mod(0) - self
        }
    }
    impl<T: ::std::convert::Into<i64>> ::std::convert::From<T> for Mod {
        fn from(v: T) -> Self {
            Mod::new(v.into())
        }
    }
}
pub type Mod = modular::Mod;


Measured memory_bytes: 41340