#if 1
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <stack>
#include <array>
#include <deque>
#include <algorithm>
#include <utility>
#include <cstdint>
#include <functional>
#include <iomanip>
#include <numeric>
#include <assert.h>
#include <bitset>
#include <list>

auto& in = std::cin;
auto& out = std::cout;
#define all_range(C) std::begin(C), std::end(C)
const double PI = 3.141592653589793238462643383279502884197169399375105820974944;

template<typename Arithmetic, typename Integral>
std::enable_if_t< std::is_unsigned<Integral>::value, Arithmetic>
ipow(Arithmetic bace, Integral n)
{
	//繰り返し二条法
	auto res = (Arithmetic)(1);
	while (n > 0) {
		if (n & 1) res *= bace;
		bace *= bace;
		n >>= 1;
	}
	return res;
}
constexpr bool is_prime(uint32_t N)
{
	if (N <= 1) {
		return false;
	}
	for (size_t i = 2; i*i <= N; ++i)
	{
		if (N%i == 0) {
			return false;
		}
	}
	return true;
}
template <uint64_t MOD> class mint_base;
//mint_base_base型用の累乗関数
template <uint64_t MOD> constexpr mint_base<MOD> m_pow(mint_base<MOD> x, uint64_t n)noexcept;
//mod計算を自動で行う整数テンプレートクラス
template <uint64_t MOD_ = 1000000007>
class mint_base
{
public:
	static constexpr auto MOD = MOD_;
	static_assert(!(MOD <= 2), "MOD cannot be below 2.");
	static_assert(MOD <= (0xFFFFFFFFFFFFFFFF / 2), "MOD is too big");//加算してオーバーフローしない
	static_assert(MOD <= 0xFFFFFFFF, "MOD is too big");//乗算してオーバーフローしない
	constexpr mint_base<MOD> operator+(const mint_base<MOD> &other)const noexcept
	{
		auto v = *this;
		return v += other;
	}
	constexpr mint_base<MOD> operator-(const mint_base<MOD> &other)const noexcept
	{
		auto v = *this;
		return v -= other;
	}
	constexpr mint_base<MOD> operator*(const mint_base<MOD> &other)const noexcept
	{
		auto v = *this;
		return v *= other;
	}
	constexpr auto operator/(const mint_base<MOD> &other)const noexcept
	{
		auto v = *this;
		return v /= other;
	}
	constexpr mint_base<MOD>& operator+=(const mint_base<MOD> &other) noexcept
	{
		a += other.a;
		if (MOD <= a) { a -= MOD; };
		return *this;
	}
	constexpr mint_base<MOD>& operator-=(const mint_base<MOD> &other) noexcept
	{
		if (a >= other.a) {
			a -= other.a;
		}
		else {
			a = (a + MOD) - other.a;
		}
		return *this;
	}
	constexpr mint_base<MOD>& operator*=(const mint_base<MOD> &other) noexcept
	{
#if 1
		a *= other.a;
		a %= MOD;
#else
		//MOD <= (MAXUINT64 / 2)条件下
		uint64_t b = other.a, v = 0;
		while (b > 0) {
			if (b & 1) {
				v += a;
				if (v >= MOD)v -= MOD;
			}
			a += a;
			if (MOD <= a)a -= MOD;
			b >>= 1;
		}
		a = v;
#endif
		return *this;
	}
	constexpr mint_base<MOD>& operator/=(const mint_base<MOD> &other) noexcept
	{
		return *this *= ~other;
	}
	constexpr mint_base<MOD> operator+()const noexcept { return *this; }
	constexpr mint_base<MOD> operator-()const noexcept
	{
		return{ MOD - a, mod_value_tag{} };
	}
	constexpr mint_base<MOD>& operator++() noexcept
	{
		if (MOD <= ++a) { a = 0; };
		return *this;
	}
	constexpr mint_base<MOD>& operator--() noexcept
	{
		if (a <= 0) { a = MOD; };
		--a;
		return *this;
	}
	constexpr mint_base<MOD> operator++(int) noexcept
	{
		auto tmp = *this;
		++*this;
		return tmp;
	}
	constexpr mint_base<MOD> operator--(int) noexcept
	{
		auto tmp = *this;
		--*this;
		return tmp;
	}
	constexpr mint_base<MOD> operator~()const noexcept
	{
		return ipow(*this, e_phi - 1);
	}
	constexpr mint_base<MOD>& operator=(const mint_base<MOD> &other) noexcept
	{
		a = other.a;
		return *this;
	}
	constexpr explicit operator uint64_t()const noexcept
	{
		return a;
	}
	constexpr explicit operator unsigned()const noexcept
	{
		return (unsigned)a;
	}
	static constexpr uint64_t getmod() noexcept
	{
		return MOD;
	}
	constexpr mint_base(uint64_t a_) noexcept :a(a_ % MOD) {}
	constexpr mint_base()noexcept : a(0) {}
	struct mod_value_tag {};
	constexpr mint_base(uint64_t a_, mod_value_tag) :a(a_) {}
private:
	static constexpr uint64_t get_e_phi()noexcept {
		//オイラー値の導出
		uint64_t temp = MOD;
		uint64_t m_ = MOD;
		for (uint64_t i = 2; i * i <= m_; ++i)
		{
			if (m_ % i == 0)
			{
				temp = temp / i * (i - 1);
				for (; m_ % i == 0; m_ /= i);
			}
		}
		if (m_ != 1)temp = temp / m_ * (m_ - 1);
		return temp;
	}
	static constexpr uint64_t e_phi = get_e_phi();//オイラー値
	uint64_t a;
};
//mint_base型用の累乗関数
template<uint64_t MOD>constexpr mint_base<MOD> m_pow(mint_base<MOD> x, uint64_t n)noexcept
{
	mint_base<MOD> res = 1;
	while (n > 0)
	{
		if (n & 1)res *= x;
		x *= x;
		n >>= 1;
	}
	return res;
}
//mint_baseの階乗計算
//O(x)時間が必要のため、fact_set関数を推奨する。
template<uint64_t MOD>constexpr mint_base<MOD> fact(mint_base<MOD> x)noexcept
{
	mint_base<MOD> res(1);
	for (uint64_t i = 1; i <= (uint64_t)x; ++i)
	{
		res *= i;
	}
	return res;
}
//mint_baseの階乗計算
//0からxまでの階乗を返す
//O(x)時間が必要
template<uint64_t MOD>std::vector<mint_base<MOD>> fact_set(mint_base<MOD> x = mint_base<MOD>(-1))
{
	mint_base<MOD> res(1);
	std::vector<mint_base<MOD>> set((uint64_t)(x)+1);
	set[0] = 1;
	for (uint64_t i = 1; i <= (uint64_t)x; ++i)
	{
		res *= i;
		set[i] = res;
	}
	return res;
}
//mint_base型のstreamへの出力
template<uint64_t MOD> std::ostream& operator<<(std::ostream& os, mint_base<MOD> i)
{
	os << (uint64_t)i;
	return os;
}
//mint_base型のstreamからの入力
template<uint64_t MOD> std::istream& operator >> (std::istream& is, mint_base<MOD>& i)
{
	uint64_t tmp;
	is >> tmp;
	i = tmp;
	return is;
}
typedef mint_base<1000000007> mint;
namespace mint_literal {
	constexpr mint operator""_mi(unsigned long long x)noexcept {
		return mint(x);
	}
}
using namespace mint_literal;
//mint_baseの階乗計算
//0からxまでの階乗を返す
//O(N)
template<int32_t X, uint64_t MOD = mint::MOD>
/*constexpr*/ std::array<mint_base<MOD>, X + 1> fact_set_c()
{
	mint_base<MOD> res(1);
	std::array<mint_base<MOD>, X + 1> set;
	set[0] = 1;
	for (int32_t i = 1; i <= X; ++i)
	{
		res *= i;
		set[i] = res;
	}
	return set;
}

template<typename T, typename U>
std::enable_if_t<std::rank<T>::value == 0> fill_all(T& arr, const U& v) {
	arr = v;
}
template<typename ARR, typename U>
std::enable_if_t<std::rank<ARR>::value != 0> fill_all(ARR& arr, const U& v) {
	for (auto& i : arr) {
		fill_all(i, v);
	}
}


int32_t N,M;
int32_t A[1000];
int32_t B[1000];

int32_t A_map[1000010];
int32_t B_map[1000010];
int main()
{
	fill_all(A_map, -1);
	fill_all(B_map, -1);

	using std::endl;
	in.sync_with_stdio(false);
	out.sync_with_stdio(false);
	in.tie(nullptr);
	out.tie(nullptr);

	in >> N>>M;
	for (size_t i = 0; i < N; i++)
	{
		in >> A[i]; A_map[A[i]] = i;
	}
	for (size_t i = 0; i < M; i++)
	{
		in >> B[i]; B_map[B[i]] = i;
	}

	mint res = 1;
	int32_t h_num = 0;//A_map
	int32_t w_num = 0;
	int32_t hw_num = 0;
	for (int32_t v = N * M;v >= 1; --v)
	{
		if (A_map[v] == -1) {
			if (B_map[v] == -1) {
				if (hw_num == 0) {
					res = 0;
					break;
				}
				res *= hw_num;
				--hw_num;
			}
			else {
				if(h_num == 0) {
					res = 0;
					break;
				}
				res *= h_num;
				++w_num;
				hw_num += (h_num-1);
			}
		}
		else {
			if (B_map[v] == -1) {
				if (w_num == 0) {
					res = 0;
					break;
				}
				res *= w_num;
				++h_num;
				hw_num += w_num-1;
			}
			else {
				hw_num += h_num;
				hw_num += w_num;
				++h_num;
				++w_num;
			}
		}
	}
	out << res << endl;

	return 0;
}
#endif


Measured memory_bytes: 8192