#include "bits/stdc++.h"

#pragma warning(disable:4996)
using namespace std;



const int mod = 1000000007;
struct Mod {
public:
	int num;
	Mod() : Mod(0) { ; }
	Mod(long long int n) : num((n % mod + mod) % mod) {
		static_assert(mod<INT_MAX / 2, "mod is too big, please make num 'long long int' from 'int'");
	}
	Mod(int n) : Mod(static_cast<long long int>(n)) { ; }
	operator int() { return num; }
};

Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator+(const Mod a, const long long int  b) { return b + a; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) { return Mod((mod + a.num - b.num) % mod); }
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) { return Mod(((long long)a.num * b.num) % mod); }
Mod operator*(const long long int a, const Mod b) { return Mod(a)*b; }
Mod operator*(const Mod a, const long long int b) { return Mod(b)*a; }
Mod operator*(const Mod a, const int b) { return Mod(b)*a; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator*=(Mod& a, const long long int &b) { return a = a * b; }
Mod operator^(const Mod a, const int n) {
	if (n == 0) return Mod(1);
	Mod res = (a * a) ^ (n / 2);
	if (n % 2) res = res * a;
	return res;
}
Mod mod_pow(const Mod a, const long long  int n) {
	if (n == 0) return Mod(1);
	Mod res = mod_pow((a * a), (n / 2));
	if (n % 2) res = res * a;
	return res;
}

//mod が素数の場合のみ　違う場合はextend euclid を用いる。
Mod inv(const Mod a) { return a ^ (mod - 2); }
Mod operator/(const Mod a, const Mod b) {
	assert(b.num != 0);
	return a * inv(b);
}
Mod operator/(const long long int a, const Mod b) {
	return Mod(a) / b;
}
Mod operator/=(Mod &a, const Mod b) {
	return a = a / b;
}

#define MAX_MOD_N 1024000

Mod fact[MAX_MOD_N], factinv[MAX_MOD_N];
void init(const int amax = MAX_MOD_N) {
	fact[0] = Mod(1); factinv[0] = 1;
	for (int i = 0; i < amax - 1; ++i) {
		fact[i + 1] = fact[i] * Mod(i + 1);
		factinv[i + 1] = factinv[i] / Mod(i + 1);
	}
}
Mod comb(const int a, const int b) {
	return fact[a] * factinv[b] * factinv[a - b];
}
int main() {
	int N,M;cin>>N>>M;
	vector<pair<int,int>>vs;
	vector<pair<int,int>>mp(N*M);
	for (int i = 0; i < N; ++i) {
		int a;cin>>a;a--;
		mp[a].first++;
	}
	for (int i = 0; i < M; ++i) {
		int b;cin>>b;b--;
		mp[b].second++;
	}
	bool ok=true;
	Mod answer=1;
	int a_free=0;
	int b_free=0;
	int ab_used=0;
	for (int i = N*M - 1; i >= 0; --i) {
		auto p(mp[i]);
		if (p.first >= 2 || p.second >= 2) {
			ok=false;
		}
		else if (p.first == 0 && p.second == 0) {
			answer*=Mod(a_free*b_free-ab_used);
			ab_used++;
		}
		else if (p.first == 1 && p.second == 0) {
			answer*=Mod(a_free);
			b_free++;
			ab_used++;

		}
		else if (p.first == 0 && p.second == 1) {
			answer*=Mod(b_free);
			a_free++;
			ab_used++;

		}
		else {
			assert(p.first == 1 && p.second == 1);
			answer*=Mod(1);
			a_free++;
			b_free++;
			ab_used++;
		}
	}
	if(!ok)answer=Mod(0);
	cout<<answer.num<<endl;
	return 0;
}


Measured memory_bytes: 16000