#include <bits/stdc++.h>

using namespace std;

#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl

typedef long long ll;
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
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); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(int i=0;i<(n);i++)
#define rep1(i,n) for(int i=1;i<=(n);i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
#define rrep1(i,n) for(int i=(n);i>0;i--)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
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; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = 1e18;
const ll MOD = 1000000007;
//const ll MOD = 998244353;
const double pi = 3.14159265358979323846;
#define Sp(p) cout<<setprecision(15)<< fixed<<p<<endl;
int dx[4] = { 1,0, -1,0 }, dy[4] = { 0,1,0,-1 };
int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
#define fio() cin.tie(0); ios::sync_with_stdio(false);
//#define mp make_pair

const int MAXN = 2000010;

vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
	ll a = 1;
	while (p) {
		if (p % 2)
			a = a*x%M;
		x = x*x%M;
		p /= 2;
	}
	return a;
}

ll mod_inverse(ll a, ll M = MOD) {
	return mod_pow(a, M - 2, M);
}

void set_fact(ll n, ll M = MOD) {
	fact[0] = fact[1] = rfact[0] = rfact[1] = 1;
	for (ll i = 2; i <= n; i++) {
		fact[i] = i * fact[i - 1] % M;
		rfact[i] = mod_inverse(fact[i], M);
	}
}

ll nCr(ll n, ll r, ll M = MOD) {
  if (r > n) return 0;
  if (n < 0 || r < 0) {
    return 0;
  }
  ll ret = fact[n];
  ret = (ret*rfact[r]) % M;
  ret = (ret*rfact[n - r]) % M;
  return ret;
}



int main() {
  set_fact(2000000);
  int h, w;
  cin >> h >> w;
  vi a(h), b(w);
  rep (i, h) {
    cin >> a[i];
  }
  rep (j, w) {
    cin >> b[j];
  }
  sort(all(a));
  reverse(all(a));
  sort(all(b));
  reverse(all(b));
  rep (i, h - 1) {
    if (a[i] == a[i + 1]) {
      cout << 0 << endl;
      return 0;
    }
  }
  rep (i, w - 1) {
    if (b[i] == b[i + 1]) {
      cout << 0 << endl;
      return 0;
    }
  }
  int nokorih = h, nokoriw = w;
  int pre = 0;
  ll nokorinum = 0;
  ll ans = 1;
  while (a[0] != inf || b[0] != inf) {
    if (a.back() < b.back()) {
      nokorinum += a.back() - pre;
      pre = a.back();
      a.pop_back();
      if (a.size() == 0) {
        a.push_back(inf);
      }
      ans = (ans * nCr(nokorinum - 1, nokoriw - 1) % MOD * fact[nokoriw] % MOD) % MOD;
      nokorih--;
      nokorinum -= nokoriw;
    }
    else if (a.back() > b.back()) {
      nokorinum += b.back() - pre;
      pre = b.back();
      b.pop_back();
      if (b.size() == 0) {
        b.push_back(inf);
      }
      ans = (ans * nCr(nokorinum - 1, nokorih - 1) % MOD  * fact[nokorih] % MOD) % MOD;
      nokoriw--;
      nokorinum -= nokorih;
    }
    else {
      nokorinum += a.back() - pre;
      pre = a.back();
      a.pop_back();
      if (a.size() == 0) {
        a.push_back(inf);
      }
      b.pop_back();
      if (b.size() == 0) {
        b.push_back(inf);
      }
      ans = (ans * nCr(nokorinum - 1, nokorih - 1) % MOD * fact[nokorih - 1] % MOD) % MOD;
      nokorinum -= nokorih;
      nokoriw--;
      ans = (ans * nCr(nokorinum, nokoriw) % MOD * fact[nokoriw] % MOD) % MOD;
      nokorinum -= nokoriw;
      nokorih--;
    }
    if (nokorinum < 0) {
      cout << 0 << endl;
      return 0;
    }
  }
  cout << ans << endl;
}


Measured memory_bytes: 31616