#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <algorithm>
#include <cmath>
#include <queue>
#include <stack>
#include <deque>
#include <cassert>
#include <complex>
#include <iomanip>
#include <random>

using namespace std;

typedef long long ll;
#define int ll

int M = (int)1e9 + 7;
#define msum(a, b) ((a) + (b) >= M ? (a) + (b) - M : (a) + (b))
#define msub(a, b) ((a) - (b) < 0 ? (a) - (b) + M : (a) - (b))
#define mmult(a, b) (((a) * (b)) % M)

typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<pii> vpi;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;
typedef complex<double> base;
typedef complex<int> point;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for(int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>


#define cerr cout
#define watch(x) cerr << (#x) << " = " << (x)    << endl;

const double PI = 2 * acos(0.0);

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream & operator << (ostream &out, pair<T0, T1> &a) {
	return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1, class T2>
inline ostream & operator << (ostream &out, tuple<T0, T1, T2> &a) {
	return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a) << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream & operator << (ostream &out, tuple<T0, T1, T2, T3> &a) {
	return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a) << ", " << get<3>(a) << "}";
}

template<class T>
inline ostream & operator << (ostream &out, vector<T> &a) {
	out << "[";
	fori(i, a.size())
		out << a[i] << vector<string>{", ", "]  "}[i + 1 == a.size()];
	return out;
}

void smain();

signed main() {
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);


	cout << setprecision(12) << fixed;
	smain();
}

#define N 400000
const int oo = (int)1e9;






void smain()
{
	int n, m;
	cin >> n >> m;
	vi a(n), b(m);
	vi row(n * m + 1), col(n * m + 1), prefc(n * m + 1), prefr(n * m + 1);
	for (int i = 0; i < n; i++) 
	{
		cin >> a[i];
		if (row[a[i]] != 0)
		{
			cout << 0;
			return;
		}
		row[a[i]] = i + 1;
	}
	for (int j = 0; j < m; j++) 
	{
		cin >> b[j];
		if (col[b[j]] != 0)
		{
			cout << 0;
			return;
		}
		col[b[j]] = j + 1;
	}

	for (int i = n * m - 1; i >= 1; i--)
	{
		prefc[i] = prefc[i + 1] + (col[i + 1] != 0);
		prefr[i] = prefr[i + 1] + (row[i + 1] != 0);
	}

	int ans = 1, pimp = 0;
	for (int i = n * m; i >= 1; i--)
	{
		if (col[i] == 0 && row[i] == 0) {
			ans = mmult(ans, msub(mmult(prefc[i], prefr[i]), pimp));
		}
		else if (col[i] == 0)
			ans = mmult(ans, prefc[i]);
		else if (row[i] == 0)
			ans = mmult(ans, prefr[i]);
		pimp++;
	}

	cout << ans;

}

//m1.codeforces.com, m2.codeforces.com или m3.codeforces.com

Measured memory_bytes: 31488