#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> void Max(T &m, const T q) { if (m < q) m = q; }
template<typename T> void Min(T &m, const T q) { if (m > q) m = q; }
template<typename T1, typename T2> pair<T1, T2> operator+(pair<T1, T2> &l, pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(pair<T1, T2> &l, pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

int N, M;
vector<lint> A, B;
map<int, int> obs;


constexpr lint MOD = 1000000007;
vector<lint> fac, facInv, inv;
void facInit(int nmax)
{
    fac = facInv = inv = vector<lint>(nmax + 1, 1);
    for (int i = 2; i <= nmax; i++)
    {
        fac[i] = fac[i-1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD;
        facInv[i] = facInv[i-1] * inv[i] % MOD;
    }
}
lint nPr(int n, int r)
{
    if (n<r || r<0) return 0;
    if (n >= (int)fac.size()) facInit(n);
    return fac[n] * facInv[n-r] % MOD;
}

void NO()
{
    puts("0");
    exit(0);
}

int main()
{

    facInit(2000000);
    cin >> N >> M;
    A.resize(N);
    B.resize(M);
    cin >> A >> B;

    for (auto v : A) obs[v] += 1;
    for (auto v : B) obs[v] += 2;

    map<int, int> coun[2];
    for (auto v : A) coun[0][v]++;
    for (auto v : B) coun[1][v]++;
    REP(d, 2) for (auto pa : coun[d]) if (pa.second > 1) NO();

    lint v0 = 0, v1 = 0;

    lint ume = 0;
    lint res = 1;
    FOR(v, 1, N * M + 1)
    {
        if (obs[v] == 0) ume++;
        else if (obs[v] == 3)
        {
            lint marg = N + M - 2 - v0 - v1;
            if (marg > ume) NO();
            res *= nPr(ume, marg);
            ume -= marg;
            v0++;
            v1++;
        }
        else if (obs[v] == 1)
        {
            lint marg = M - v1;

            res *= marg;
            marg--;

            res %= MOD;
            if (marg > ume) NO();
            res *= nPr(ume, marg);
            ume -= marg;
            v0++;
        }
        else if (obs[v] == 2)
        {
            lint marg = N - v0;

            res *= marg;
            marg--;

            res %= MOD;
            if (marg > ume) NO();
            res *= nPr(ume, marg);
            ume -= marg;
            v1++;
        }

        res %= MOD;
    }

    cout << res << endl;
}


Measured memory_bytes: 94080