#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};
#[allow(unused_imports)]
use std::io::{stdout, stdin, BufWriter, Write};

pub fn uppper_bound<T: Ord>(a: &Vec<T>, x: &T) -> usize {
    use std::cmp::Ordering;
    let mut l = 0;
    let mut r = a.len();
    while l != r {
        let m = l + (r - l) / 2;
        match a[m].cmp(x) {
            Ordering::Less | Ordering::Equal => l = m + 1,
            Ordering::Greater => r = m,
        }
    }
    l
}


fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (write!(out,$($format)*).unwrap());
    }

    input!{
      n: usize,
      m: usize,
      mut aa: [usize;n],
      mut bb: [usize;m],
    }
    use std::collections::HashSet;

    aa.sort();
    aa.dedup();
    let sa: HashSet<_> = aa.iter().map(|&v|v).collect();
    bb.sort();
    bb.dedup();
    let sb: HashSet<_> = bb.iter().map(|&v|v).collect();
    if aa.len() != n || bb.len() != m {
        return puts!("{}\n", 0);
    }

    const MOD: usize = 1e9 as usize + 7;
    let mut ans = 1;
    for i in (1..n*m+1).rev() {
        if sa.contains(&i) && sb.contains(&i) {
            continue;
        }
        if sa.contains(&i) {
            let pos = m - uppper_bound(&bb, &i);
            ans *= pos;
            ans %= MOD;
        } else if sb.contains(&i) {
            let pos = n - uppper_bound(&aa, &i);
            ans *= pos;
            ans %= MOD;
        } else {
            let pos1 = n - uppper_bound(&aa, &i);
            let pos2 = m - uppper_bound(&bb, &i);

            // debug!(aa, bb);
            // debug!(i, pos1, pos2);

            ans *= (pos1 * pos2) - (n*m - i);
            ans %= MOD;
        }
    }
    puts!("{}\n", ans);
}


Measured memory_bytes: 4476