#include <bits/stdc++.h>
using namespace std;

#define pb push_back
#define mp make_pair
#define rep(i,n) for(int i = 0; i < (n); i++)
#define repr(i,b,e) for(int i = (b); i <= (e); i++)

#define pr(x) do{cerr << (#x) << " = " << (x) << endl;}while(0)
#define pri(x,i) do{cerr << (#x) << "[" << i << "] = " << (x[i]) << endl;}while(0)

namespace std {
	template<class S, class T> pair<S, T> operator + (const pair<S, T> &a, const pair<S, T> &b) {return mp<S, T>(a.first + b.first, a.second + b.second);}
	template<class S, class T> pair<S, T> operator - (const pair<S, T> &a, const pair<S, T> &b) {return mp<S, T>(a.first - b.first, a.second - b.second);}
	template<class S, class T> pair<S, T>& operator += (pair<S, T> &a, const pair<S, T> &other) {return a = a + other;}
	template<class S, class T> pair<S, T>& operator -= (pair<S, T> &a, const pair<S, T> &other) {return a = a - other;}
	template<class S, class T> ostream& operator << (ostream& ost, pair<S, T> p) {ost << "(" << p.first << ", " << p.second << ")";return ost;}
	template<class T> ostream& print_iterable_container(ostream& ost, T& container) {
		for (auto&& iter = begin(container); iter != end(container); ++iter) ost << (iter == begin(container) ? " [ " : ", ") << (*iter);
		return ost << " ]";
	}
#	define APPLY_PRINT_ITERABLE_CONTAINER(container_type)\
	template<class T> ostream& operator << (ostream& ost, container_type<T>& container) {\
		return print_iterable_container(ost, container);\
	}
	APPLY_PRINT_ITERABLE_CONTAINER(vector);
	APPLY_PRINT_ITERABLE_CONTAINER(list);
	APPLY_PRINT_ITERABLE_CONTAINER(deque);
}

template<class T> inline bool CHMAX(T &l,const T &r){return l<r?l=r,1:0;}
template<class T> inline bool CHMIN(T &l,const T &r){return l>r?l=r,1:0;}

using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vi>;
using vvll = vector<vll>;
using vpii = vector<pii>;
using vpll = vector<pll>;

using ld = long double;

template<class T> using VV = vector<vector<T> >;
template<class T> using maxPQ = priority_queue<T>;
template<class T> using minPQ = priority_queue<T, vector<T>, greater<T> >;
template<class T, class U> using uomap = unordered_map<T, U>;
template<class T> using uoset = unordered_set<T>;

const ll INF = 1001001001;
const ll INFll = (ll)INF * INF;
const ll MOD = 1000000007;
const ll MOD_FFT = 998244353;
const ld EPS = 1e-15;

//function<void(int,int)> tensi_no_3p=[&](int v,int d){
//};

int main() {
	ios_base::sync_with_stdio(false);
	int N, M; cin >> N >> M;
	vi A(N); rep(i, N) cin >> A[i];
	vi B(M); rep(i, M) cin >> B[i];
	set<int> rows, cols;
	rep(i, N) rows.insert(A[i]);
	rep(i, M) cols.insert(B[i]);
	int usedr = 0, usedc = 0;
	ll ans = 1;
	for (int n = N * M; n >= 1; n--) {
		bool hitr = rows.find(n) != rows.end();
		bool hitc = cols.find(n) != cols.end();
		if (hitr && hitc) {
			usedr++;
			usedc++;
		}
		else if (hitr) {
			usedr++;
			ans = ans * usedc % MOD;
		}
		else if (hitc) {
			usedc++;
			ans = ans * usedr % MOD;
		}
		else {
			int t = N * M - n;
			ans = ans * max(0, usedc * usedr - t)  % MOD;
		}
	}
	if (usedr != N || usedc != M) ans = 0;
	cout << ans << endl;
	return 0;
}


Measured memory_bytes: 384