#include<bits/stdc++.h>
#include<iostream>
#include<cstdio>
#include<vector>
#include<string>
#include<algorithm>
#include<map>
using namespace std;
#define rep(i,x) for(ll i = 0; i < (ll)(x); i++)
#define rrep(i,x) for(ll i = (ll)(x)-1;0 <= i; i--)
#define reps(i,x) for(ll i = 1; i < (ll)(x)+1; i++)
#define rreps(i,x) for(ll i = (ll)(x); 1 <= i; i--)
#define debug(x) cerr << #x << ": " << (x) << "\n";
#define all(x) (x).begin(), (x).end()
typedef long long ll;
typedef long double ld;
typedef pair<int,int> P;
typedef pair<ll,ll> Pll;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef vector<vector<vector<ll>>> vvvl;
const ll INF = numeric_limits<ll>::max()/4;
const int n_max = 1e6+10;

template<std::int_fast64_t Modulus>
class modint {
    using i64 = int_fast64_t;

    public:
    i64 a;

    constexpr modint(const i64 x = 0) noexcept {
        this -> a = x % Modulus;
        if(a < 0){
            a += Modulus;
        }
    }
    constexpr i64 &value() const noexcept {return a;}
    // constexpr const i64 &value() const noexcept {return a;}
    constexpr modint operator+(const modint rhs) const noexcept {
        return modint(*this) += rhs;
    }
    constexpr modint operator-(const modint rhs) const noexcept {
        return modint(*this) -= rhs;
    }
    constexpr modint operator*(const modint rhs) const noexcept {
        return modint(*this) *= rhs;
    }
    constexpr modint operator/(const modint rhs) const noexcept {
        return modint(*this) /= rhs;
    }
    constexpr modint &operator+=(const modint rhs) noexcept {
        a += rhs.a;
        if(a >= Modulus) {
            a -= Modulus;
        }
        return *this;
    }
    constexpr modint &operator-=(const modint rhs) noexcept {
        if(a < rhs.a) {
            a += Modulus;
        }
        a -= rhs.a;
        return *this;
    }
    constexpr modint &operator*=(const modint rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    constexpr modint &operator/=(modint rhs) noexcept {
        i64 a_ = rhs.a, b = Modulus, u = 1, v = 0;
        while(b){
            i64 t = a_/b;
            a_ -= t * b; swap(a_,b);
            u -= t * v; swap(u,v);
        }
        a = a * u % Modulus;
        if(a < 0) a += Modulus;
        return *this;
    }
    
    // 自前実装
    constexpr bool operator==(const modint rhs) noexcept {
        return a == rhs.a;
    }
    constexpr bool operator!=(const modint rhs) noexcept {
        return a != rhs.a;
    }
    constexpr bool operator>(const modint rhs) noexcept {
        return a > rhs.a;
    }
    constexpr bool operator>=(const modint rhs) noexcept {
        return a >= rhs.a;
    }
    constexpr bool operator<(const modint rhs) noexcept {
        return a < rhs.a;
    }
    constexpr bool operator<=(const modint rhs) noexcept {
        return a <= rhs.a;
    }
    constexpr modint& operator++() noexcept {
        return (*this) += modint(1);
    }
    constexpr modint operator++(int) {
        modint tmp(*this);
        operator++();
        return tmp;
    }
    constexpr modint& operator--() noexcept {
        return (*this) -= modint(1);
    }
    constexpr modint operator--(int) {
        modint tmp(*this);
        operator--();
        return tmp;
    }
    template<typename T>
    friend constexpr modint modpow(modint &mt, T n) noexcept {
        if(n < 0){
            modint t = (modint(1) / mt);
            return modpow(t, -n);
        }
        modint res = 1;
        while(n){
            if(n & 1)res *= mt;
            mt *= mt;
            n /= 2;
        }
        return res;
    }
};

const ll MOD = 1e9+7;
using mint = modint<MOD>;
// 標準入出力対応
std::ostream &operator<<(std::ostream &out, const modint<MOD> &m) {
    out << m.a;
    return out;
}
std::istream &operator>>(std::istream &in, modint<MOD> &m) {
    ll a;
    in >> a;
    m = mint(a);
    return in;
}

int main(){
    ll n,m; cin >> n >> m;
    vector<ll> a(n);
    rep(i,n) cin >> a[i];
    vector<ll> b(m);
    rep(i,m) cin >> b[i];
    vector<ll> h(n_max,0), h_sum(n_max+1,0);
    vector<ll> v(n_max,0), v_sum(n_max+1,0);
    bool ok = true;
    rep(i,n){
        if(h[a[i]-1])ok = false;
        h[a[i]-1]++;
    }
    rep(i,m){
        if(v[b[i]-1])ok = false;
        v[b[i]-1]++;
    }
    rreps(i,n_max)h_sum[i-1] = h_sum[i] + h[i-1];
    rreps(i,n_max)v_sum[i-1] = v_sum[i] + v[i-1];
    mint ans = 1;
    rrep(i,m*n){
        // debug(i);debug(h[i]);debug(v[i]);
        if(h[i] || v[i]){
            if(h[i] && v[i])continue;
            if(h[i])ans *= mint(v_sum[i]);
            if(v[i])ans *= mint(h_sum[i]);
        }
        else{
            ans *= mint(h_sum[i] * v_sum[i] - (n*m - i - 1));
        }
        // debug(i);debug(ans);
    }

    cout << (ok ? ans : mint(0)) << endl;

}

Measured memory_bytes: 31616