#include <iostream>
#include <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep_r(i, n) for (int i = n - 1; i >= 0; i--)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define REP(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i)
#define all(x) (x).begin(), (x).end()
#define SZ(x) ((ll)(x).size())
#define bit(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());

#define INF bit(60)
#define pb push_back
#define mod 1000000007

using namespace std;
using uif = uint_fast64_t;
using ll = long long int;
using tTree = __gnu_pbds::tree<ll, __gnu_pbds::null_type, less<ll>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

ll dx[4] = {1, 0, -1, 0};
ll dy[4] = {0, 1, 0, -1};

#define FACSIZE 200002

ll invfac[FACSIZE];
ll fac[FACSIZE];

template <class T>
bool chmax(T &, const T &);
template <class T>
bool chmin(T &, const T &);
ll gcd(ll, ll);
ll powLL(ll x, ll y);

ll mod_pow(ll, ll);
ll mod_add(ll, ll);
ll mod_mul(ll, ll);
ll mod_div(ll, ll);
ll comb(ll, ll);
void make_fact(ll);
void make_invfact(ll);
void fact_init();

int main(void)
{
  ll n, m;
  cin >> n >> m;
  vector<ll> A(n);
  vector<ll> B(m);
  rep(i, n) cin >> A[i];
  rep(i, m) cin >> B[i];

  //vector<ll> row(n);
  //vector<ll> col(m);
  ll Rf = 0;
  ll Cf = 0;

  priority_queue<ll> Rque;
  priority_queue<ll> Cque;

  rep(i, n) Rque.push(A[i]);
  rep(i, m) Cque.push(B[i]);

  //vector<ll> Rnum(n, m);
  //vector<ll> Cnum(m, n);

  //if( Rque.size()!= )

  ll ans = 1;

  for (ll i = n * m; i > 0; i--)
  {
    bool Re = false, Ce = false;
    if (!Rque.empty() && Rque.top() == i)
    {
      Rf++;
      auto q = Rque.top();
      Rque.pop();
      if (!Rque.empty() && Rque.top() == q)
      {
        cout << 0 << endl;
        return 0;
      }
      Re = true;
    }
    if (!Cque.empty() && Cque.top() == i)
    {
      Cf++;
      auto q = Cque.top();
      Cque.pop();
      if (!Cque.empty() && Cque.top() == q)
      {
        cout << 0 << endl;
        return 0;
      }
      Ce = true;
    }

    //cout << i << endl;

    if (Re && Ce)
    {
      //cout << "case1" << endl;
      //cout << 1 << endl;
      //ans = mod_mul(ans, mod_add(mod_mul(Rf, Cf), -(n * m - i)));
    }
    else if (Re || Ce)
    {

      if (Re)
      {
        //cout << "case2" << endl;
        //cout << m - Cque.size() << endl;

        ans = mod_mul(ans, m - Cque.size());
      }
      else
      {
        //cout << "case3" << endl;
        //cout << n - Rque.size() << endl;
        ans = mod_mul(ans, n - Rque.size());
      }
    }
    else
    {
      //cout << "case4" << endl;
      //cout << mod_add(mod_mul(Rf, Cf), -(n * m - i)) << endl;
      ans = mod_mul(ans, mod_add(mod_mul(Rf, Cf), -(n * m - i)));
    }
  }

  cout << ans << endl;

  return 0;
}

ll mod_pow(ll x, ll r)
{
  if (r == 0)
    return 1;
  else if (r == 1)
    return x % mod;
  else if (r % 2 == 0)
  {
    ll t = mod_pow(x, r / 2) % mod;
    return mod_mul(t, t);
  }
  else
  {
    ll t = mod_pow(x, r / 2) % mod;
    ll k = mod_mul(t, t);
    return (k % mod) * (x % mod);
  }
}
ll mod_add(ll a, ll b)
{
  return (((mod + a) % mod) + ((b + mod) % mod)) % mod;
}

ll mod_mul(ll a, ll b)
{
  return ((a % mod) * (b % mod)) % mod;
}

ll mod_div(ll a, ll b)
{
  return mod_mul(a, mod_pow(b, mod - 2));
}

void fact_init()
{
  make_fact(FACSIZE - 1);
  make_invfact(FACSIZE);
}

void make_fact(ll n)
{
  fac[0] = 1;
  rep(i, n)
  {
    fac[i + 1] = mod_mul(fac[i], i + 1);
  }
}

void make_invfact(ll n)
{
  invfac[n] = mod_pow(fac[n], mod - 2);
  for (int i = n - 1; i >= 0; i--)
  {
    invfac[i] = mod_mul(invfac[i + 1], i + 1);
  }
}

ll comb(ll n, ll r)
{

  return mod_mul(mod_mul(fac[n], invfac[r]), invfac[n - r]);
}
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;
}

ll qp(ll a, ll b)
{
  ll ans = 1LL;
  do
  {
    if (b & 1LL)
      ans = 1LL * mod_mul(ans, a) % mod;
    a = 1LL * mod_mul(a, a) % mod;
  } while (b >>= 1LL);
  return ans;
}
ll qp(ll a, ll b, ll mo)
{
  ll ans = 1LL;
  do
  {
    if (b & 1LL)
      ans = 1LL * (ans % mo) * (a % mo);
    a = 1LL * (a % mo) * (a % mo);
  } while (b >>= 1LL);
  return ans;
}
ll gcd(ll a, ll b)
{
  return b ? gcd(b, a % b) : a;
}
ll powLL(ll x, ll y)
{
  ll ans = 1LL;
  for (ll i = 0LL; i < y; i++)
    ans *= x;
  return ans;
}


Measured memory_bytes: 256