#include <bits/stdc++.h>
using namespace std;
template <class T> inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T> inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return 1;
    }
    return 0;
}
void print() { cout << "\n"; }
template <class T> void print(const T &x) { cout << x << "\n"; }
template <class T, class... Args> void print(const T &x, const Args &... args) {
    cout << x << " ";
    print(args...);
}
template <class T> void printVector(const vector<T> &v) {
    for(const T &x : v) {
        cout << x << " ";
    }
    cout << "\n";
}
using ll = long long;

#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
const double EPS = 1e-7;
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
const double PI = acos(-1);
constexpr int MOD = 1000000007;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

//-------------------------------------
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 mint = ModInt<MOD>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n, m;
    cin >> n >> m;
    vector<int> a(n), b(m);
    for(int i = 0; i < n; i++) {
        cin >> a[i];
    }
    for(int i = 0; i < m; i++) {
        cin >> b[i];
    }
    mint ans = 1;
    int cntN = 0, cntM = 0, free = 0;
    vector<bool> existN(n * m + 1, 0), existM(n * m + 1, 0);
    for(int i = 0; i < n; i++) {
        if(existN[a[i]]) {
            print(0);
            return 0;
        }
        existN[a[i]] = 1;
    }
    for(int i = 0; i < m; i++) {
        if(existM[b[i]]) {
            print(0);
            return 0;
        }
        existM[b[i]] = 1;
    }
    for(int i = n * m; i >= 1; i--) {
        if(existN[i] && existM[i]) {
            free += (cntN + cntM);
            cntN++, cntM++;
        } else if(existN[i]) {
            ans *= cntM;
            free += (cntM - 1);
            cntN++;
        } else if(existM[i]) {
            ans *= cntN;
            free += (cntN - 1);
            cntM++;
        } else {
            ans *= free;
            free--;
        }
    }
    print(ans);
}


Measured memory_bytes: 512