// ===== 2019/01/13 21:33:58 =====

// includes.hpp

#include <algorithm>
#include <array>
#include <cassert>
#include <climits>
#include <complex>
#include <cstdio>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <string>
#include <tuple>
#include <vector>

// cin.cpp

template <typename T, int M, int N> struct tuple_getter {
  static void get(std::istream &is, T &x) {
    is >> std::get<M>(x);
    tuple_getter<T, M + 1, N>::get(is, x);
  }
};

template <typename T, int N> struct tuple_getter<T, N, N> {
  static void get(std::istream &is, T &x) { is >> std::get<N>(x); }
};

template <typename... Args>
std::istream &operator>>(std::istream &is, std::tuple<Args...> &t) {
  tuple_getter<std::tuple<Args...>, 0, sizeof...(Args) - 1>::get(is, t);
  return is;
}

template <typename T, typename U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
  for (T &x : v) is >> x;
  return is;
}

// const_value.hpp

namespace sub {
template <typename T>
constexpr typename std::enable_if<std::is_integral<T>::value, T>::type
inf_sub() {
  return std::numeric_limits<T>::max() / 2 - 1000;
}

template <typename T>
constexpr typename std::enable_if<std::is_floating_point<T>::value, T>::type
inf_sub() {
  return std::min(std::numeric_limits<T>::max() / 2 - 1000, T(1e50));
}
}  // namespace sub

template <typename T> constexpr T inf() {
  static_assert(std::is_arithmetic<T>::value, "T must be arithmetic value");
  return sub::inf_sub<T>();
}

template <typename T> constexpr T zero() {
  static_assert(std::is_arithmetic<T>::value, "T must be arithmetic value");
  return T(0);
}

const long double pi = acos(-1.0);

// cout.cpp

template <typename T, int M, int N> struct tuple_printer {
  static void print(std::ostream &os, const T &x) {
    os << std::get<M>(x) << " ";
    tuple_printer<T, M + 1, N>::print(os, x);
  }
};

template <typename T, int N> struct tuple_printer<T, N, N> {
  static void print(std::ostream &os, const T &x) { os << std::get<N>(x); }
};

template <typename... Args>
std::ostream &operator<<(std::ostream &os, const std::tuple<Args...> &t) {
  tuple_printer<std::tuple<Args...>, 0, sizeof...(Args) - 1>::print(os, t);
  return os;
}

template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
  for (auto it = v.begin(); it != v.end(); ++it) {
    if (it != v.begin()) os << " ";
    os << *it;
  }
  return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::set<T> &v) {
  for (auto it = v.begin(); it != v.end(); ++it) {
    if (it != v.begin()) os << " ";
    os << *it;
  }
  return os;
}

// initialize.cpp

struct yes_no : std::numpunct<char> {
  string_type do_truename() const { return "Yes"; }
  string_type do_falsename() const { return "No"; }
};

struct Initialize {
  Initialize() {
    std::locale loc(std::locale(), new yes_no);
    std::cout << std::boolalpha << std::setprecision(11) << std::fixed;
    std::cout.imbue(loc);
  }
};

const Initialize initialize;

// macros.hpp

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

// misc.hpp

template <typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }

template <typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }

// range.hpp

class range {
  class index_type {
    int x;

  public:
    index_type(int x_) : x(x_) {}
    int operator*() const { return x; }
    bool operator!=(index_type &r) { return x < r.x; }
    void operator++() { ++x; }
  };
  index_type i, n;

public:
  range(int n_) : i(0), n(n_) {}
  range(int i_, int n_) : i(i_), n(n_) {}
  index_type &begin() { return i; }
  index_type &end() { return n; }
};

// typedef.hpp

using ll = long long;
using ld = long double;

// template.cpp

using namespace std;

// mod.cpp

template <int M, bool IsPrime = false> class Modulo {
  int n;
  static typename std::enable_if<IsPrime, ll>::type inv(ll a, ll p) {
    return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
  }

public:
  Modulo() : n(0) { ; }
  Modulo(int m) : n(m) {
    if (n >= M)
      n %= M;
    else if (n < 0)
      n = (n % M + M) % M;
  }
  Modulo(ll m) {
    if (m >= M)
      m %= M;
    else if (m < 0)
      m = (m % M + M) % M;
    n = m;
  }
  explicit operator int() const { return n; }
  explicit operator ll() const { return n; }
  bool operator==(const Modulo &a) const { return n == a.n; }
  Modulo &operator+=(const Modulo &a) {
    n += a.n;
    if (n >= M) n -= M;
    return *this;
  }
  Modulo &operator-=(const Modulo &a) {
    n -= a.n;
    if (n < 0) n += M;
    return *this;
  }
  Modulo &operator*=(const Modulo &a) {
    n = (ll(n) * a.n) % M;
    return *this;
  }
  Modulo operator+(const Modulo &a) const {
    Modulo res = *this;
    return res += a;
  }
  Modulo operator-(const Modulo &a) const {
    Modulo res = *this;
    return res -= a;
  }
  Modulo operator-() const { return Modulo(0) - *this; }
  Modulo operator*(const Modulo &a) const {
    Modulo res = *this;
    return res *= a;
  }
  Modulo operator^(ll m) const {
    if (m == 0) return Modulo(1);
    const Modulo a = *this;
    Modulo res = (a * a) ^ (m / 2);
    return m % 2 ? res * a : res;
  }
  typename std::enable_if<IsPrime, Modulo>::type
  operator/(const Modulo &a) const {
    return *this * inv(ll(a), M);
  }
  typename std::enable_if<IsPrime, Modulo>::type operator/=(const Modulo &a) {
    return *this *= inv(ll(a), M);
  }
};

template <int M, bool IsPrime = false> bool is_zero(Modulo<M, IsPrime> x) {
  return int(x) == 0;
}
template <int M, bool IsPrime = false> int abs(Modulo<M, IsPrime> x) {
  return int(x);
}

const int mod = 1000000007;

template <int M = mod> Modulo<M, true> fact(int n, bool sw = true) {
  static std::vector<Modulo<M, true>> v1 = { 1 }, v2 = { 1 };
  if (n >= (int)v1.size()) {
    const int from = v1.size(), to = n + 1024;
    v1.reserve(to);
    v2.reserve(to);
    for (int i = from; i < to; ++i) {
      v1.push_back(v1.back() * Modulo<M, true>(i));
      v2.push_back(v2.back() / Modulo<M, true>(i));
    }
  }
  return sw ? v1[n] : v2[n];
}

template <int M = mod> Modulo<M, true> comb(ll a, ll b) {
  if (b < 0 || b > a) return 0;
  return fact<M>(a, true) * fact<M>(b, false) * fact<M>(a - b, false);
}

using Mod = Modulo<mod, true>;

// D.cpp

template<typename T>
vector<T> table(int n, T v) { return vector<T>(n, v); }

template <class... Args>
auto table(int n, Args... args) {
  auto val = table(args...);
  return vector<decltype(val)>(n, move(val));
}

int r[1024000];
int c[1024000];

void solve(ll N, ll M, vector<ll> A, vector<ll> B) {
  memset(r, -1, sizeof(r));
  memset(c, -1, sizeof(c));
  REP(i,N) r[A[i] - 1] = i;
  REP(i,M) c[B[i] - 1] = i;
  int rc = 0, cc = 0;
  int cnt = 0;
  Mod res = 1;
  for (int i = N * M - 1; i >= 0; --i) {
    if (r[i] == -1 && c[i] == -1) {
      res *= (rc * cc - cnt);
      ++cnt;
    }
    else if (r[i] == -1) {
      res *= cc;
      ++rc;
      ++cnt;
    }
    else if (c[i] == -1) {
      res *= rc;
      ++cc;
      ++cnt;
    }
    else {
      ++rc;
      ++cc;
      ++cnt;
    }
    // cout << rc << " " << cc << endl;
  }
  cout << int(res) << endl;
}

int main() {
	ll N;
	ll M;
	scanf("%lld", &N);
	vector<ll> A(N-1+1);
	scanf("%lld", &M);
	vector<ll> B(M-1+1);
	for (int i = 0 ; i <= N-1 ; i++) {
	  scanf("%lld", &A[i]);
	}
	for (int i = 0 ; i <= M-1 ; i++) {
	  scanf("%lld", &B[i]);
	}
	solve(N, M, A, B);
	return 0;
}

// ===== 2019/01/13 21:33:58 =====


Measured memory_bytes: 8320