#include <bits/stdc++.h>
using namespace std;
#define int long long
#define PI 3.141592653589793
#define rep(i, n) for (int i = 0; i < (n); i++)
#define REP(i, a, n) for (int i = a; i < (n); i++)
#define rrep(i, n, k) for (int i = (n); i >= (k); i--);
#define all(x) (x).begin(), (x).end()
#define vi vector<int>
template<class T> istream &operator>>(istream&is,vector<T>&v){for(auto &elemnt:v)is>>elemnt;return is;}
template<class T,class U> istream &operator>>(istream&is,pair<T,U>&p){is>>p.first>>p.second;return is;}
template<class T>vector<T> make_vector(size_t a){return vector<T>(a);}
template<class T, class... Ts>auto make_vector(size_t a, Ts... ts){return vector<decltype(make_vector<T>(ts...))>(a, make_vector<T>(ts...));}
const int MOD = 1e9 + 7;
const int INF = 2e18;

template< int mod >
struct ModInt {
    int x;

    ModInt() : x(0) {}

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p) {
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }

    ModInt operator-() const { return ModInt(-x); }

    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 x == p.x; }

    bool operator!=(const ModInt &p) const { return x != p.x; }

    ModInt inverse() const {
        int a = x, 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(int64_t n) const {
        ModInt ret(1), mul(x);
        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.x;
    }

    friend istream &operator>>(istream &is, ModInt &a) {
        int64_t t;
        is >> t;
        a = ModInt< mod >(t);
        return (is);
    }

    static int get_mod() { return mod; }
};

using modint = ModInt< MOD >;


signed main() {
    int N, M;
    cin >> N >> M;
    vector<int> A(N), B(M);
    cin >> A >> B;
    map<int, int> check;
    set<int> fix;
    for (int i = 0; i < N; i++) for (int j = 0; j < M; j++) {
        if (A[i] == B[j]) {
            if (fix.find(A[i]) != fix.end()) {
                cout << 0 << endl;
                return 0;
            }
            fix.insert(A[i]);
        }
        check[min(A[i], B[j])]++;
    }
    modint ans = 1;
    int temp = 0;
    for (int i = N * M; i >= 1; i--) {
        temp += check[i];
        if (fix.find(i) != fix.end()) {
            temp--;
            continue;
        }
        if (check[i] != 0) {
            ans *= check[i];
            temp--;
        } else ans *= temp--;
    }
    cout << ans << endl;
}


Measured memory_bytes: 62848