#include <algorithm>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using namespace std;
#define rep(i, n) for(int(i) = 0; (i) < (n); (i)++)
#define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++)
#define All(v) (v).begin(), (v).end()
#define pb push_back
#define MP(a, b) make_pair((a), (b))
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int INF = 1 << 30;
const ll LINF = 1LL << 60;
const int MOD = 1e9 + 7;

template <uint_fast64_t MOD> class ModInt {
    using u64 = uint_fast64_t;

  public:
    u64 val;

    ModInt(const u64 x = 0) : val(x % MOD) {}
    constexpr u64 &value() { return val; }
    constexpr ModInt operator-() { return val ? MOD - val : 0; }
    constexpr ModInt operator+(const ModInt &rhs) const {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt &rhs) const {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt &rhs) const {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt &rhs) const {
        return ModInt(*this) /= rhs;
    }
    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if(val >= MOD) {
            val -= MOD;
        }
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if(val < rhs.val) {
            val += MOD;
        }
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = val * rhs.val % MOD;
        return *this;
    }

    constexpr ModInt &operator/=(const ModInt &rhs) {
        *this *= rhs.inv();
        return *this;
    }

    constexpr bool operator==(const ModInt &rhs) { return this->a == rhs.a; }
    constexpr bool operator!=(const ModInt &rhs) { return this->a != rhs.a; }
    friend constexpr ostream &operator<<(ostream &os, const ModInt<MOD> &x) {
        return os << x.val;
    }
    friend constexpr istream &operator>>(istream &is, ModInt<MOD> &x) {
        return is >> x.val;
    }

    constexpr ModInt inv() const {
        u64 x = val, y = MOD, u = 1, v = 0, t = 0;
        while(y > 0) {
            t = x / y;
            x -= t * y;
            swap(x, y);
            u -= t * v;
            swap(u, v);
        }
        return ModInt(u);
    }

    constexpr ModInt pow(int e) const {
        u64 x = 1, p = val;
        while(e > 0) {
            if(e % 2 == 0) {
                p = (p * p) % MOD;
                e /= 2;
            } else {
                x = (x * p) % MOD;
                e--;
            }
        }
        return ModInt(x);
    }
};

using mint = ModInt<MOD>;

int main() {
    ll N, M;
    cin >> N >> M;
    vector<ll> A(N), B(M);
    mint res = 1;
    rep(i, N) cin >> A[i];
    rep(i, M) cin >> B[i];
    sort(A.rbegin(), A.rend());
    sort(B.rbegin(), B.rend());
    bool ok = 1;
    rep(i, N - 1) {
        if(A[i] == A[i + 1])
            ok = 0;
    }
    rep(i, M - 1) {
        if(B[i] == B[i + 1])
            ok = 0;
    }
    if(!ok || A.front() != N * M || B.front() != N * M) {
        cout << 0 << endl;
        return 0;
    }
    int Acur = 0, Bcur = 0;
    for(int num = N * M - 1, cnt = 1; num >= 1; num--, cnt++) {
        while(Acur + 1 < N && A[Acur + 1] >= num)
            Acur++;
        while(Bcur + 1 < M && B[Bcur + 1] >= num)
            Bcur++;
        if(A[Acur] == num && B[Bcur] == num) {
        } else if(A[Acur] == num) {
            res *= mint(Bcur + 1);
        } else if(B[Bcur] == num) {
            res *= mint(Acur + 1);
        } else {
            res *= mint((Acur + 1) * (Bcur + 1) - cnt);
        }
    }
    cout << res << endl;
    return 0;
}

Measured memory_bytes: 3596