#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<int, int> Pi;
typedef vector<ll> Vec;
typedef vector<int> Vi;
typedef vector<string> Vs;
typedef vector<vector<ll>> VV;
typedef vector<vector<int>> VVi;

#define REP(i, a, b) for(ll i=(a); i<(b); i++)
#define PER(i, a, b) for(ll i=(a); i>=(b); i--)
#define rep(i, n) REP(i, 0, n)
#define per(i, n) PER(i, n, 0)
const ll INF=1e16+18;
const ll MAX=100005;
const ll MOD=1000000007;
#define Yes(n) cout << ((n) ? "Yes" : "No") << endl;
#define YES(n) cout << ((n) ? "YES" : "NO") << endl;
#define ALL(v) v.begin(), v.end()
#define rALL(v) v.rbegin(), v.rend()
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp(a, b) make_pair(a,b)
#define Each(a,b) for(auto &a :b)
#define REPM(i, mp) for (auto i = mp.begin(); i != mp.end(); ++i)
#define dbg(x_) cerr << #x_ << ":" << x_ << endl;
#define dbgmap(mp) cerr << #mp << ":"<<endl; for (auto i = mp.begin(); i != mp.end(); ++i) { cerr << i->first <<":"<<i->second << endl;}
#define dbgarr(n,m,arr) rep(i,n){rep(j,m){cerr<<arr[i][j]<<" ";}cerr<<endl;}
#define dbgdp(n,arr) rep(i,n){cerr<<arr[i]<<" ";}cerr<<endl;
#define sum(v) accumulate(ALL(v),0)
#define fi first
#define se second

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }

template<typename T1, typename T2>
ostream &operator<<(ostream &s, const pair<T1, T2> &p) { return s<<"("<<p.first<<", "<<p.second<<")"; }

// vector
template<typename T>
ostream &operator<<(ostream &s, const vector<T> &v) {
    int len=v.size();
    for(int i=0; i<len; ++i) {
        s<<v[i];
        if(i<len-1) s<<"	";
    }
    return s;
}

// 2 dimentional vector
template<typename T>
ostream &operator<<(ostream &s, const vector<vector<T> > &vv) {
    int len=vv.size();
    for(int i=0; i<len; ++i) {
        s<<vv[i]<<endl;
    }
    return s;
}

struct mint {
    ll x; // typedef long long ll;
    mint(ll x=0):x((x%MOD+MOD)%MOD){}
    mint& operator+=(const mint a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator-=(const mint a) {
        if ((x += MOD-a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator*=(const mint a) {
        (x *= a.x) %= MOD;
        return *this;
    }
    mint operator+(const mint a) const {
        mint res(*this);
        return res+=a;
    }
    mint operator-(const mint a) const {
        mint res(*this);
        return res-=a;
    }
    mint operator*(const mint a) const {
        mint res(*this);
        return res*=a;
    }
    mint pow(ll t) const {
        if (!t) return 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 res(*this);
        return res/=a;
    }
};

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout<<std::setprecision(10);

    ll n,m;
    cin>>n>>m;
    Vec a(n);
    Vec b(m);
    rep(i,n){
        cin>>a[i];
    }
    rep(i,m){
        cin>>b[i];
    }
    sort(ALL(a));
    sort(ALL(b));

    rep(i,n-1){
        if(a[i+1]==a[i]){
            cout<<0<<endl;
            return 0;
        }
    }

    rep(i,m-1){
        if(b[i+1]==b[i]){
            cout<<0<<endl;
            return 0;
        }
    }

    mint ans = 1;

    ll cnt = 0;
    PER(i,n*m,1){
        bool exia = binary_search(ALL(a),i);
        bool exib = binary_search(ALL(b),i);

        auto aitr = upper_bound(ALL(a),i);
        auto bitr = upper_bound(ALL(b),i);
        ll acount = n - (aitr-a.begin());
        ll bcount = m - (bitr-b.begin());
//        dbg(acount);
//        dbg(bcount);
//        dbg(cnt);
        if(exia && exib){
            //1通り
        }else if(exib){
            if(aitr==a.end()){
                cout<<0<<endl;
                return 0;
            }
            ans *= acount;
        }else if(exia){
            if(bitr==b.end()){
                cout<<0<<endl;
                return 0;
            }
            ans *= bcount;
        }else{
            if(aitr==a.end()){
                cout<<0<<endl;
                return 0;
            }
            if(bitr==b.end()){
                cout<<0<<endl;
                return 0;
            }
            ans *= (acount*bcount-cnt);
        }
      //  dbg(ans.x);
        cnt++;
    }
    cout<<ans.x<<endl;
    return  0;
}


Measured memory_bytes: 256