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//
#include <bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<(b);++i)
#define erep(i,a,b) for(int i=a;i<=(b);++i)
#define per(i,a,b) for(int i=(a);i>(b);--i)
#define eper(i,a,b) for(int i=(a);i>=b;--i)
#define fore(i, x, a) for(auto &&x:a) 
#define ITR(i,b,e) for(auto i=(b);i!=(e);++i)
#define IN(i,a,b) (a)<=(i) && (i)<(b)
#define debug(x)  cout << #x << " = " << (x) << endl;
#define pb push_back
#define mp make_pair
#define MOD 1000000007
#define ALL(x) begin(x),end(x)
#define F first
#define S second
#define debug(x)  cout << #x << " = " << (x) << endl;
const int inf=1001001001; const long long INF=1001001001001001001;
using namespace std;
using ll = long long;
using Pii = pair<int,int>;
using vii = vector<int>;
using vll = vector<ll>;
template<class T>using  PS_queue = priority_queue<T, vector<T>, greater<T> >;
template<class T>using vv = vector<T>;
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; }
template<typename A, size_t N, typename T> void Fill(A (&array)[N], const T &val){fill( (T*)array, (T*)(array+N), val );}
template<class T> ostream& operator<<(ostream &os,const vector<T> &v) {
    ITR(i,begin(v),end(v))os<<*i<<(i==end(v)-1?"":" ");return os;}
template<class T> istream& operator>>(istream &is,vector<T> &v) {
    ITR(i,begin(v),end(v)) is>>*i;return is;}
template<class T,class U> istream& operator>>(istream &is, pair<T,U> &p) {
    is>>p.first>>p.second;return is;}
template<class T>T gcd(T a, T b){ return b ? gcd(b, a % b) : a; }
template<class T>T lcm(T a, T b){ return a / gcd(a, b) * b; }
struct edge { int to, from, cost; };
int dy[]={0, 1, -1, 0}; int dx[]={1, 0, 0, -1};

int n, m;
int main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
  cin >> n >> m;
  vll a(n+1), b(m+1);
  rep(i, 0, n) cin >> a[i];
  rep(i, 0, m) cin >> b[i];
  sort(ALL(a), greater<int>()); 
  sort(ALL(b), greater<int>());
  ll ans = 1;
  int xa = 0, xb = 0;
  eper(x, n * m, 1) {
    if (a[xa] > x || b[xb] > x) {
      cout << 0 << endl;
      return 0;
    }
    ll t = 1;
    if (a[xa] == x && b[xb] == x) {
      t = 1;
      xa++, xb++;
    } else if (a[xa] == x) {
      t = xb;
      xa++;
    } else if (b[xb] == x) {
      t = xa;
      xb++;
    } else {
      t = xa * xb - (n * m - x);
      if (t <= 0) {
        cout << 0 << endl;
        return 0;
      }
    }
    ans = (ans * t) % MOD;
  }
  cout << ans << endl;
  return 0;
}



Measured memory_bytes: 256