#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include <algorithm>
#include <cassert>
#include <cfloat>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

using namespace std;

#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define repLRE(i, l, r) for (ll i = (l); i <= (r); ++i)
#define rrepLRE(i, l, r) for (ll i = (l); i >= (r); --i)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define Lower_bound(v, x) \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))

using ll = long long;
using ull = unsigned long long;
using P = pair<ll, ll>;
using T = tuple<ll, ll, ll>;
using vll = vector<ll>;
using vP = vector<P>;
using vT = vector<T>;
using vvll = vector<vector<ll>>;
using vvP = vector<vector<P>>;
using dqll = deque<ll>;

ll dx[9] = {-1, 1, 0, 0, -1, -1, 1, 1, 0};
ll dy[9] = {0, 0, -1, 1, -1, 1, -1, 1, 0};

/* Macros reg. ends here */

const ll INF = 1LL << 50;

static const long long mod = 1000000007;
struct mint {
  ll x;
  mint(ll x = 0) : x(x % mod) {}
  mint& operator+=(const mint a) {
    (x += a.x) %= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    (x += mod - a.x) %= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint ret(*this);
    return ret += a;
  }
  mint operator-(const mint a) const {
    mint ret(*this);
    return ret -= a;
  }
  mint operator*(const mint a) const {
    mint ret(*this);
    return ret *= a;
  }
  mint pow(ll t) const {
    if (t == 0) return mint(1);
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint& operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint ret(*this);
    return ret /= a;
  }
};
class modutils {
  vector<mint> fact, invfact;

 public:
  modutils(int n = 200005) : fact(n + 1), invfact(n + 1) {
    fact[0] = 1;
    for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i;
    invfact[n] = fact[n].inv();
    for (int i = n; i >= 1; i--) invfact[i - 1] = invfact[i] * i;
  }
  mint pow(mint x, ll n) { return x.pow(n); }
  mint comb(ll n, ll k) {
    if (n < 0 || k < 0 || n < k) return 0;
    return fact[n] * invfact[k] * invfact[n - k];
  }
  mint perm(ll n, ll k) {
    if (n < 0 || k < 0 || n < k) return 0;
    return fact[n] * invfact[n - k];
  }
  mint fac(ll n) { return fact[n]; }
};

int main() {
  // ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cout << fixed << setprecision(15);

  ll n, m;
  cin >> n >> m;
  vll as(n), bs(m);
  rep(i, n) cin >> as[i];
  rep(i, m) cin >> bs[i];
  sort(as.begin(), as.end());
  sort(bs.begin(), bs.end());
  ll siz = 0, presiz = 0;
  ll cand = 0;
  bool ok = as.back() == n * m && bs.back() == n * m;
  rep(i, n - 1) ok &= as[i] < as[i + 1];
  rep(i, m - 1) ok &= bs[i] < bs[i + 1];
  if(!ok){
    puts("0");
    return 0;
  }
  mint ans(1);
  rrepLRE(i, m * n, 1) {
    ll y = Lower_bound(as, i);
    ll x = Lower_bound(bs, i);
    presiz = siz;
    siz = (n - y) * (m - x);
    cand += siz - presiz;
    ll mulv;
    if (as[y] == i && bs[x] != i)
      mulv = m - x;
    else if (as[y] != i && bs[x] == i)
      mulv = n - y;
    else if (as[y] == i && bs[x] == i)
      mulv = 1;
    else
      mulv = cand;
    ans *= mulv;
    cand--;
  }

  cout << ans.x << endl;

  return 0;
}


Measured memory_bytes: 384