#[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>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

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

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

pub mod modular {
    const M: i64 = 1000000007;

    #[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
        }

        // This requires M is prime
        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())
        }
    }
}

use modular::Mod;
use std::collections::BTreeMap;

fn main() {
    input! {
        n: usize,
        m: usize,
        a: [usize; n],
        b: [usize; m],
    }

    let mut sa = BTreeMap::new();
    let mut sb = BTreeMap::new();

    for &r in a.iter() {
        *sa.entry(r).or_insert(0) += 1;
    }
    for &r in b.iter() {
        *sb.entry(r).or_insert(0) += 1;
    }

    for (_, v) in sa.iter() {
        if *v >= 2 {
            println!("0");
            return;
        }
    }

    for (_, v) in sb.iter() {
        if *v >= 2 {
            println!("0");
            return;
        }
    }

    let mut use_n = 0;
    let mut use_m = 0;
    let mut placed = 0;
    let mut ans = Mod::new(1);

    for i in (1..n * m + 1).rev() {
        let fa = sa.contains_key(&i);
        let fb = sb.contains_key(&i);

        if fa && fb {
            use_n += 1;
            use_m += 1;
        } else if fa {
            use_n += 1;
            ans *= Mod::new(use_m);
        } else if fb {
            use_m += 1;
            ans *= Mod::new(use_n);
        } else {
            if use_m * use_n > placed {
                ans *= Mod::new(use_m * use_n - placed);
            } else {
                ans = Mod::new(0);
            }
        }

        // println!("{:?}", ans);

        placed += 1;
    }

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


Measured memory_bytes: 4352