#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; i < (n); i++)
#define RREP(i, n) for (int i = (n); i >= 0; i--)
#define FOR(i, m, n) for (int i = (m); i < (n); i++)
#define ALL(obj) begin(obj), end(obj)
using namespace std;
using ll = long long;
using ull = unsigned long long;

const int INF = 2100100100;
const int MOD = 1e9 + 7;

// 多次元 vector 生成
template <class T> vector<T> make_vec(size_t a) { return vector<T>(a); }
template <class T, class... Ts> auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <class T> bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T> bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}

template <int mod> struct ModInt {
    int val;
    ModInt() : val(0) {}
    ModInt(long long x) : val(x >= 0 ? x % mod : (mod - (-x) % mod) % mod) {}
    ModInt &operator+=(const ModInt &p) {
        if ((val += p.val) >= mod) {
            val -= mod;
        }
        return *this;
    }
    ModInt &operator-=(const ModInt &p) {
        if ((val += mod - p.val) >= mod) {
            val -= mod;
        }
        return *this;
    }
    ModInt &operator*=(const ModInt &p) {
        val = (int)(1LL * val * p.val % mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }
    ModInt operator-() const { return ModInt(-val); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return val == p.val; }
    bool operator!=(const ModInt &p) const { return val != p.val; }
    ModInt inverse() const {
        int a = val, b = mod, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }
    ModInt pow(long long n) const {
        ModInt ret(1), mul(val);
        while (n > 0) {
            if (n & 1)
                ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.val; }
    friend istream &operator>>(istream &is, ModInt &a) {
        long long t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }
    static int get_mod() { return mod; }
};
using modint = ModInt<MOD>;

int main() {
    // cin.tie(0);
    // ios::sync_with_stdio(false);
    int N, M;
    cin >> N >> M;
    vector<int> A(N);
    vector<int> B(M);
    REP(i, N) { cin >> A.at(i); }
    REP(i, M) { cin >> B.at(i); }
    A.push_back(-1);
    B.push_back(-1);
    sort(ALL(A), greater<int>());
    sort(ALL(B), greater<int>());

    int a_i = 0;
    int b_i = 0;
    modint ans = modint(1);
    for (int x = N * M; x > 0; x--) {
        while (A[a_i] > x) {
            a_i++;
        }
        while (B[b_i] > x) {
            b_i++;
        }
        if (A[a_i] == B[b_i] && A[a_i] == x) {
            if ((a_i + 1 < N && A[a_i + 1] == A[a_i]) || (b_i + 1 < M && B[b_i + 1] == B[b_i])) {
                cout << 0 << endl;
                return 0;
            }
        } else if (A[a_i] == x) {
            ans *= modint(b_i);
        } else if (B[b_i] == x) {
            ans *= modint(a_i);
        } else {
            ans *= (modint(a_i) * modint(b_i) - modint(N * M - x));
        }
    }

    cout << ans.val << endl;
    return 0;
}


Measured memory_bytes: 764