#include <bits/stdc++.h>
#include <sys/time.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>;
ll ugauss(ll a, ll b) { if (!a) return 0; if (a>0^b>0) return a/b; else return (a+(a>0?-1:1))/b+1; }
ll lgauss(ll a, ll b) { if (!a) return 0; if (a>0^b>0) return (a+(a>0?-1:1))/b-1; else return a/b; }
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T> ostream &operator<<(ostream &o, const deque<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const unordered_set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U, typename V>  ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; }
template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;}
template <typename T, typename S, typename U> ostream &operator<<(ostream &o, const priority_queue<T, S, U> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const queue<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.front(); tmp.pop(); o << x << " ";} return o; }
template <typename T> ostream &operator<<(ostream &o, const stack<T> &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} return o; }
template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;};
void vizGraph(vvll& g, int mode = 0, string filename = "out.png") { ofstream ofs("./out.dot"); ofs << "digraph graph_name {" << endl; set<P> memo; rep(i, g.size())  rep(j, g[i].size()) { if (mode && (memo.count(P(i, g[i][j])) || memo.count(P(g[i][j], i)))) continue; memo.insert(P(i, g[i][j])); ofs << "    " << i << " -> " << g[i][j] << (mode ? " [arrowhead = none]" : "")<< endl;  } ofs << "}" << endl; ofs.close(); system(((string)"dot -T png out.dot >" + filename).c_str()); }
struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; }
size_t random_seed; struct init_{init_(){ ios::sync_with_stdio(false); cin.tie(0); gettimeofday(&start, NULL); struct timeval myTime; struct tm *time_st; gettimeofday(&myTime, NULL); time_st = localtime(&myTime.tv_sec); srand(myTime.tv_usec); random_seed = RAND_MAX / 2 + rand() / 2; }} init__;
#define ldout fixed << setprecision(40) 

#define EPS (double)1e-14
#define INF (ll)1e18
#define mo  (ll)(1e9+7)

ll brutal(ll n, ll m, vll a, vll b) {
    vll id;
    ll ret = 0;
    rep(i, n*m) id.pb(i);
    do {
        vll ac(n);
        vll bc(m);
        rep(i, n*m) {
            chmax(ac[i/m], id[i]);
            chmax(bc[i%m], id[i]);
        }
        ret += (a == ac) && (b == bc);
    } while (next_permutation(all(id)));
    return ret;
}

int main(void) {
    ll n, m; cin >> n >> m;
    vll a(n); cin >> a;
    vll b(m); cin >> b;
    rep(i, n) a[i]--;
    rep(i, m) b[i]--;
    sort(all(a));
    sort(all(b));
    set<ll> as; rep(i, n) as.insert(a[i]);
    set<ll> bs; rep(i, m) bs.insert(b[i]);
//    cout << a << endl;
//    cout << b << endl;
    if (as.size() != n || bs.size() != m) {
        cout << 0 << endl;
        return 0;
    }

    vll freq(n*m); rep(i, n) rep(j, m) freq[min(a[i], b[j])]++;
    ll ret = 1;
    ll cnt = 0;
    for (ll i = n * m - 1; i >= 0; i--) {
        cnt += freq[i];
        if (as.count(i) && bs.count(i)) {
        } else if (!as.count(i) && !bs.count(i)) {
            (ret *= cnt) %= mo;
//            cout << i<< " " << cnt << endl;
        } else if (as.count(i)) {
            (ret *= m - (ll)(lower_bound(all(b), i) - b.begin())) %= mo;
//            cout << i << " " << (ll)(lower_bound(all(b), i) - b.begin()) << endl;
        } else {
            (ret *= n - (ll)(lower_bound(all(a), i) - a.begin())) %= mo;
//            cout << i << " " << (ll)(lower_bound(all(a), i) - a.begin()) << endl;
        }
        cnt--;
//        cout << ret << endl;
    }
    cout << ret << endl;

    /*
    auto br = brutal(n, m, a, b);
    if (ret != br) {
        cout << "##################" << endl;
        cout << a << " " << b << endl;
        cout << ret << " " << br << endl;
    }
    */

    return 0;
}


Measured memory_bytes: 8188