#include <iostream>
#include <iomanip>
#include <string>
#include <cmath>
#include <climits>
#include <algorithm>
#include <cassert>
#include <vector>
#include <array>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <stack>
#include <queue>
#include <numeric>
#define ALL(c) (c).begin(), (c).end()

using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdi = pair<double, int>;
using pdd = pair<double, double>;

#pragma once

#include <vector>

unsigned int mod;
struct Modint;
std::vector<Modint> fact_mod;
std::vector<Modint> rev_fact_mod;

using namespace std;

template<typename Tint>
Tint gcd(Tint a, Tint b) {
	// O(log max(a,b))
	return b != 0 ? gcd(b, a % b) : a;
}

template<typename Tint>
Tint lcm(Tint a, Tint b) {
	return a / gcd(a, b) * b;
}

// a x + b y = gcd(a, b)
int extgcd(const unsigned int a, const unsigned int b, int &x, int &y) {
	// O(log max(a,b))
	int g = a; x = 1; y = 0;
	if (b != 0) g = extgcd(b, a % b, y, x), y -= (a / b) * x;
	return g;
}

void set_mod(const unsigned int m) {
	mod = m;
}
void set_mod(const int m) {
	if (m > 0)
		set_mod((unsigned int)m);
	else
		cout << "Error in set_mod" << endl;
}

unsigned int inv_mod(const unsigned int a) {
	int x, y;
	if (extgcd(a, mod, x, y) == 1)
		return (unsigned int)(((long long)x + mod) % mod);
	else // unsolvable
		return 0;
}

struct Modint {
	unsigned int value;
	Modint() : Modint(0) { }
	Modint(unsigned int value) : value(value%mod) {	}
	Modint(int value) : Modint((unsigned int)(value % mod + mod)) {	}
	Modint(const Modint& rhs) : Modint(rhs.value) { }
	Modint& operator+=(const Modint& rhs);
	Modint& operator+=(const unsigned int rhs);
	Modint& operator+=(const int rhs);
	Modint& operator-=(const Modint& rhs);
	Modint& operator-=(const unsigned int rhs);
	Modint& operator-=(const int rhs);
	Modint& operator*=(const Modint& rhs);
	Modint& operator*=(const unsigned int rhs);
	Modint& operator*=(const int rhs);
	Modint& operator/=(const Modint& rhs);
	Modint& operator/=(const unsigned int rhs);
	Modint& operator/=(const int rhs);
};
Modint& Modint::operator+=(const Modint& rhs)
{
	(*this) += rhs.value;
	return *this;
}
Modint& Modint::operator+=(const unsigned int rhs)
{
	unsigned long long tmp = this->value;
	tmp += rhs;
	tmp %= mod;
	this->value = (unsigned int)tmp;
	return *this;
}
Modint& Modint::operator+=(const int rhs)
{
	(*this) += (unsigned int)(rhs % mod + mod);
	return *this;
}
Modint& Modint::operator-=(const Modint& rhs)
{
	(*this) -= rhs.value;
	return *this;
}
Modint& Modint::operator-=(const unsigned int rhs)
{
	*this += mod - rhs % mod;
	return *this;
}
Modint& Modint::operator-=(const int rhs)
{
	*this -= (unsigned int)(rhs % mod + mod);
	return *this;
}
Modint& Modint::operator*=(const Modint& rhs)
{
	(*this) *= rhs.value;
	return *this;
}
Modint& Modint::operator*=(const unsigned int rhs)
{
	unsigned long long tmp = this->value;
	tmp *= rhs;
	tmp %= mod;
	this->value = (unsigned int)tmp;
	return *this;
}
Modint& Modint::operator*=(const int rhs)
{
	(*this) *= (unsigned int)(rhs % mod + mod);
	return *this;
}
Modint& Modint::operator/=(const Modint& rhs)
{
	(*this) /= rhs.value;
	return *this;
}
Modint& Modint::operator/=(const unsigned int rhs)
{
	*this *= inv_mod(rhs);
	return *this;
}
Modint& Modint::operator/=(const int rhs)
{
	*this /= (unsigned int)(rhs % mod + mod);
	return *this;
}
const Modint operator + (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) += rhs;
}
const Modint operator + (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) += rhs;
}
const Modint operator + (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) += rhs;
}
const Modint operator - (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) -= rhs;
}
const Modint operator - (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) -= rhs;
}
const Modint operator - (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) -= rhs;
}
const Modint operator * (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) *= rhs;
}
const Modint operator * (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) *= rhs;
}
const Modint operator * (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) *= rhs;
}
const Modint operator / (const Modint& lhs, const Modint& rhs) {
	return Modint(lhs) /= rhs;
}
const Modint operator / (const Modint& lhs, unsigned int rhs) {
	return Modint(lhs) /= rhs;
}
const Modint operator / (unsigned int lhs, const Modint& rhs) {
	return Modint(lhs) /= rhs;
}
ostream& operator<<(std::ostream& lhs, const Modint& rhs)
{
	lhs << rhs.value;
	return lhs;
}

Modint pow_mod(const Modint& x, const unsigned int k) { //x^k (mod)
	if (k == 0)     return Modint(1);
	if (k % 2 == 0) return pow_mod(x*x, k / 2);
	else            return x * pow_mod(x, k - 1);
}
Modint pow_mod(const unsigned int x, const unsigned int k) {
	return pow_mod(Modint(x), k);
}

std::vector<Modint> set_fact_mod(unsigned int n) {
	fact_mod = vector<Modint>(n + 1);
	fact_mod[0] = 1;
	for (unsigned int i = 1; i <= n; i++)
	{
		fact_mod[i] = fact_mod[i - 1] * i;
	}
	return fact_mod;
}

std::vector<Modint> set_rev_fact_mod(unsigned int n) {
	rev_fact_mod = vector<Modint>(n + 1);
	rev_fact_mod[n] = 1 / fact_mod[n];
	for (int i = n - 1; i >= 0; i--)
	{
		rev_fact_mod[i] = rev_fact_mod[i + 1] * (unsigned int)(i + 1);
	}
	return rev_fact_mod;
}

Modint combination_mod_precalculation(unsigned int n, unsigned int r) {
	//set mod, fact_mod, rev_fact_mod
	return fact_mod[n] * rev_fact_mod[r] * rev_fact_mod[n - r];
}

Modint combination_mod_straightforward(unsigned int n, unsigned int r) { //mod is prime
	if (r * 2 > n) r = n - r;
	Modint numerator = 1;
	Modint denominator = 1;
	for (unsigned int i = 1; i <= r; ++i) {
		numerator *= n - i + 1;
		denominator *= i;
	}
	return numerator / denominator;
}

int N, M;
vector<int> A, B;

#define MOD 1000000007

int main() {
	cin >> N >> M;
	for (int i = 0; i < N; i++)
	{
		int tmpA;
		cin >> tmpA;
		A.push_back(tmpA);
	}
	for (int j = 0; j < M; j++)
	{
		int tmpB;
		cin >> tmpB;
		B.push_back(tmpB);
	}

	const int NM = N * M;
	unordered_set<int> uma, umb;
	for (int i = 0; i < N; i++)
	{
		int a = NM - A[i];
		if (uma.find(a) != uma.end()) {
			cout << 0 << endl;
			return 0;
		}
		uma.insert(NM - A[i]);
	}
	for (int j = 0; j < M; j++)
	{
		int b = NM - B[j];
		if (umb.find(b) != umb.end()) {
			cout << 0 << endl;
			return 0;
		}
		umb.insert(NM - B[j]);
	}

	set_mod(MOD);
	Modint ans = 1;
	int c_gyou = 0;
	int c_retsu = 0;
	for (int k = 0; k < NM; k++)
	{
		if (uma.find(k) != uma.end()) { //tateyoko
			c_gyou += 1;
			if (umb.find(k) != umb.end()) {
				c_retsu += 1;
				ans *= 1;
			}
			else {
				if (c_retsu <= 0) {
					ans = 0;
					break;
				}
				ans *= c_retsu;
			}
		}
		else {
			if (umb.find(k) != umb.end()) {
				c_retsu += 1;
				if (c_gyou <= 0) {
					ans = 0;
					break;
				}
				ans *= c_gyou;
			}
			else {
				if (c_gyou * c_retsu - k <= 0) {
					ans = 0;
					break;
				}
				ans *= c_gyou * c_retsu - k;
			}
		}
	}
	cout << ans << endl;
}


Measured memory_bytes: 384