#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef unsigned int uint;
typedef unsigned char uchar;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

#define REP(i,x) for(int i=0;i<(int)(x);i++)
#define REPS(i,x) for(int i=1;i<=(int)(x);i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RREPS(i,x) for(int i=((int)(x));i>0;i--)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();i++)
#define RFOR(i,c) for(__typeof((c).rbegin())i=(c).rbegin();i!=(c).rend();i++)
#define ALL(container) (container).begin(), (container).end()
#define RALL(container) (container).rbegin(), (container).rend()
#define SZ(container) ((int)container.size())
#define mp(a,b) make_pair(a, b)
#define pb push_back
#define eb emplace_back
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define __builtin_popcount __builtin_popcountll

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 (a>b) { a=b; return 1; } return 0; }
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
    os<<"["; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"]"; return os;
}
template<class T> ostream& operator<<(ostream &os, const set<T> &t) {
    os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os;
}
template<class S, class T> ostream& operator<<(ostream &os, const map<S, T> &t) {
    os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os;
}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}
template<class S, class T> pair<S,T> operator+(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S,T> operator-(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first-t.first, s.second-t.second);}

const int INF = 1<<28;
const double EPS = 1e-8;
const int MOD = 1000000007;


int T, n, m;

int main(int argc, char *argv[]){
    ios::sync_with_stdio(false);
    string s;
    while(cin >> n >> m){
        vi a(n), b(m);
        REP(i, n) cin >> a[i];
        REP(j, m) cin >> b[j];
        sort(RALL(a));
        sort(RALL(b));
        int p = n * m;
        int empty = 0, nxt = n * m;
        ll ans = 1;
        for(int i = 0, j = 0; p > 0; p --) {
            if ((i < n && a[i] > p) || (j < m && b[j] > p)) {
                ans = 0;
                break;
            }
            if ((i >= n || a[i] != p) && (j >= m || b[j] != p)) {
                continue;
            }
            while(nxt > p) {
                ans = ans * empty % MOD;
                empty --;
                nxt --;
            }
            nxt --;
            if (i < n && j < m && a[i] == p && b[j] == p) {
                empty += i + j;
                i ++; j ++;
            } else if (i < n && a[i] == p) {
                ans = ans * j % MOD;
                empty += j - 1;
                i ++;
            } else if (j < m && b[j] == p) {
                ans = ans * i % MOD;
                empty += i - 1;
                j ++;
            }
        }
        while(nxt > 0) {
            ans = ans * empty % MOD;
            empty --;
            nxt --;
        }
        cout << ans << endl;
    }
    return 0;
}


Measured memory_bytes: 256