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

template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
    return '"' + s + '"';
}

string to_string(const char* s) {
    return to_string((string) s);
}

string to_string(bool b) {
     return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
    bool first = true;
    string res = "{";
    for (int i = 0; i < static_cast<int>(v.size()); i++) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(v[i]);
    }
    res += "}";
    return res;
}

template <size_t N>
string to_string(bitset<N> v) {
    string res = "";
    for (size_t i = 0; i < N; i++) {
        res += static_cast<char>('0' + v[i]);
    }
    return res;
}

template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
            first = false;
            res += to_string(x);
    }
    res += "}";
    return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
    return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
    return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

#define rep(i,n) for (int i = 0; i < n; ++i)
#define reps(i,s,n) for (int i = s; i < n; ++i)
#define rep1(i,n) for (int i = 1; i <= n; ++i)
#define per(i,n) for (int i = n - 1; i >= 0; --i)
#define per1(i,n) for (int i = n; i >= 1; --i)
#define all(c) begin(c),end(c)
template<typename T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<typename T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<typename T> inline T intceil(T a, T b) { return (a + (b - 1)) / b; }
typedef long long ll;
typedef long double ld;
typedef pair<int,int> P;
typedef tuple<int,int,int> Tint;
typedef pair<ll,ll> PL;
const long long MOD = 1e9+7;
#define precout() cout << std::fixed << std::setprecision(20);
#define print(a) cout << a << endl;
template<typename T> void printv(vector<T>&v) {
    int n = v.size() - 1;
    rep(i, n) cout << v[i] << " ";
    cout << v.back() << endl;
}
const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const int dy[4] = { 0, 1, 0, -1 };
const int dx[4] = { 1, 0, -1, 0 };
// if(nextH >= 0 && nextH < H && nextW >= 0 && nextW < W)
static const long double pi = acos(-1.0);
typedef complex<ld> cd;

int N, M;
vector<int> A, B;

long long solve() {
    long long res = 1;
    int biggerX_a = 0, biggerX_b = 0; // A, B で x より大きいのが何個あるか
    for (int x = N*M; x >= 1; --x) {
        if (A[biggerX_a] > x) return 0;
        if (B[biggerX_b] > x) return 0;

        long long tmp = 1;
        if (A[biggerX_a] == x && B[biggerX_b] == x) {
            tmp = 1;
            ++biggerX_a, ++biggerX_b;
        }
        else if (A[biggerX_a] == x) {
            tmp = biggerX_b;
            ++biggerX_a;
        }
        else if (B[biggerX_b] == x) {
            tmp = biggerX_a;
            ++biggerX_b;
        }
        else {
            tmp = biggerX_a * biggerX_b - (N * M - x);
            if (tmp <= 0) return 0;
        }
        res = (res * tmp) % MOD;
    }
    return res;
}
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cin >> N >> M;
    A.resize(N + 1); B.resize(M + 1);
    for (int i = 0; i < N; ++i) cin >> A[i];
    for (int i = 0; i < M; ++i) cin >> B[i];
    sort(A.begin(), A.end(), greater<int>());
    sort(B.begin(), B.end(), greater<int>());
    cout << solve() << endl;
}


Measured memory_bytes: 3668