use std::collections::BTreeMap;
fn solve() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let m: usize = sc.read();
    let a: Vec<usize> = sc.vec(n);
    let b: Vec<usize> = sc.vec(m);
    let mut rows_count = BTreeMap::new();
    let mut cols_count = BTreeMap::new();
    for &x in a.iter() {
        *cols_count.entry(x).or_insert(0) += 1;
    }
    for &x in b.iter() {
        *rows_count.entry(x).or_insert(0) += 1;
    }
    for (_, v) in cols_count.iter() {
        if *v >= 2 {
            println!("0");
            return;
        }
    }
    for (_, v) in rows_count.iter() {
        if *v >= 2 {
            println!("0");
            return;
        }
    }
    let mut result = mod_int::ModInt::<usize>::new(1);
    let mut use_n = 0;
    let mut use_m = 0;
    let mut placed = 0;
    for x in (1..n * m + 1).rev() {
        let r = rows_count.contains_key(&x);
        let c = cols_count.contains_key(&x);

        if r && c {
            use_n += 1;
            use_m += 1;
        } else if r {
            use_m += 1;
            result *= use_n;
        } else if c {
            use_n += 1;
            result *= use_m;
        } else {
            if use_m * use_n > placed {
                result *= use_n * use_m - placed;
            } else {
                println!("0");
                return;
            }
        }
        placed += 1;
    }
    println!("{}", result.0);
}

fn main() {
    std::thread::Builder::new()
        .stack_size(64 * 1024 * 1024) // 64MB
        .spawn(|| solve())
        .unwrap()
        .join()
        .unwrap();
}

pub mod mod_int {
    use std::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign};

    //we may need to change this value
    const MOD: i64 = 1e9 as i64 + 7;

    #[derive(Clone, Copy, Debug)]
    pub struct ModInt<T: Copy + Clone + Add + AddAssign + Mul + MulAssign + Sub + SubAssign>(pub T);

    #[warn(unused_macros)]
    macro_rules! mod_int_impl {
        ($($t:ty)*) => ($(
            impl Add<ModInt<$t>> for ModInt<$t> {
                type Output = ModInt<$t>;
                fn add(self, other: ModInt<$t>) -> ModInt<$t> {
                    self + other.0
                }
            }
            impl Add<$t> for ModInt<$t> {
                type Output = ModInt<$t>;
                fn add(self, rhs: $t) -> ModInt<$t> {
                    let mut tmp = rhs + self.0;
                    if tmp >= self::MOD as $t {
                        tmp = tmp - self::MOD as $t;
                    }
                    ModInt(tmp)
                }
            }
            impl Sub<ModInt<$t>> for ModInt<$t> {
                type Output = ModInt<$t>;
                fn sub(self, rhs: ModInt<$t>) -> ModInt<$t> {
                    self - rhs.0
                }
            }
            impl Sub<$t> for ModInt<$t> {
                type Output = ModInt<$t>;
                fn sub(self, rhs: $t) -> ModInt<$t> {
                    let rhs = if rhs >= self::MOD as $t { rhs % self::MOD as $t} else { rhs };
                    let value = if self.0 < rhs { self.0 + self::MOD as $t} else { self.0 };
                    ModInt(value - rhs)
                }
            }
            impl AddAssign<ModInt<$t>> for ModInt<$t> {
                fn add_assign(&mut self, rhs: ModInt<$t>) {
                    *self = *self + rhs;
                }
            }
            impl AddAssign<$t> for ModInt<$t> {
                fn add_assign(&mut self, rhs: $t) {
                    *self = *self + rhs;
                }
            }
            impl SubAssign<ModInt<$t>> for ModInt<$t> {
                fn sub_assign(&mut self, rhs: ModInt<$t>) {
                    *self = *self - rhs;
                }
            }

            impl SubAssign<$t> for ModInt<$t> {
                fn sub_assign(&mut self, rhs: $t) {
                    *self = *self - rhs;
                }
            }

            impl Mul<ModInt<$t>> for ModInt<$t> {
                type Output = ModInt<$t>;
                fn mul(self, rhs: ModInt<$t>) -> ModInt<$t> {
                    self * rhs.0
                }
            }
            impl Mul<$t> for ModInt<$t> {
                type Output = ModInt<$t>;
                fn mul(self, rhs: $t) -> ModInt<$t> {
                    ModInt(self.0 * rhs % self::MOD as $t)
                }
            }
            impl MulAssign<ModInt<$t>> for ModInt<$t> {
                fn mul_assign(&mut self, rhs: ModInt<$t>) {
                    *self = *self * rhs;
                }
            }

            impl MulAssign<$t> for ModInt<$t> {
                fn mul_assign(&mut self, rhs: $t) {
                    *self = *self * rhs;
                }
            }
            impl ModInt<$t> {
                pub fn new(x: $t) -> Self {
                    ModInt(x)
                }
                pub fn pow(self, e: usize) -> ModInt<$t> {
                    let mut result = ModInt::<$t>::new(1);
                    let mut cur = self;
                    let mut e = e;
                    while e > 0 {
                        if e & 1 == 1 {
                            result *= cur;
                        }
                        cur *= cur;
                        e >>= 1;
                    }
                    result
                }
            }
            )*)
    }
    mod_int_impl!(usize i32 i64 u32 u64);
}

//snippet from kenkoooo
pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn read_line(&mut self) -> String {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b'\n' || b == b'\r')
            .take_while(|&b| b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }

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


Measured memory_bytes: 8572