#include <iostream>
#include <string>
#include <algorithm>
#include <functional>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <cstdio>
#include <cmath>
#include <tuple>
#include <iomanip>
#include <numeric>
#include <unordered_map>
#include <sstream>
#include<limits.h>
#include<float.h>
#include<list>
#include <array>
#include <complex>
#include<stdio.h>
#include<string.h>
#include <bitset>
#include<assert.h>

using namespace std;
#define int long long

#define I32_MAX 2147483647
#define I64_MAX 9223372036854775807LL
#define I64_MAX2 1223372036854775807LL
#define INF I64_MAX2
#define MOD 1000000007


#define MEM_SIZE 10000
#define DEBUG_OUT true
#define ALL(x) (x).begin(), (x).end()

template<typename T> void DEBUG(T e){if(DEBUG_OUT == false)return; std::cout << e <<" ";}
template<typename T> void DEBUG(const std::vector<T>& v){if(DEBUG_OUT == false)return;for(const auto& e : v){std::cout<< e << " "; } std::cout << std::endl;}
template<typename T> void DEBUG(const std::vector<std::vector<T> >& vv){if(DEBUG_OUT == false)return;for(const auto& v : vv){ DEBUG(v); } }
template<class T,class... Ts> void DEBUG(T d, Ts... e){if(DEBUG_OUT == false)return;DEBUG(d);DEBUG(e...);}
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; abort();}}
template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }


//BELOW
struct mint
{
  int x; // typedef long long int;
  mint(int 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(int 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;
  }
};

const int MAX = 510000;

long long fac[MAX], finv[MAX], inv[MAX];
// テーブルを作る前処理
void COMinit()
{
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++)
  {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

int COM(int n, int k)
{
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int PERM(int n, int k)
{
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[n - k] % MOD) % MOD;
}

int MCOM(int n, int k)
{
  //n個のものから重複を許してr個選ぶ。
  //Choose R from N types of things, allowing for duplication.
  return COM(n + k - 1, k);
}
//solve

//-----CODE------//



void solve(void)
{
  int N;cin>>N;
  int M;cin>>M;
  vector<int> A (N,0);
  set<int> CA,CB;
  int flag = 1;
  for (int i = 0; i < N; i++)
  {
     cin>>A[i];
    auto r = CA.insert(A[i]);
    if(r.second == false) flag = 0;
     
  }
  vector<int> B (M,0);
  for (int i = 0; i < M; i++)
  {
     cin>>B[i];
    auto r = CB.insert(B[i]);
    if(r.second == false) flag = 0;
  }

  mint res = 1;
  res *= flag;

    sort(ALL(A));
    sort(ALL(B));
  for (int x = N*M; x >= 1; x--) 
  {
    int iA = -1;
    int iB = -1;
    for (int i = 0; i < N; i++)
    {
      if(x == A[i]) iA = i;
    }

    for (int i = 0; i < M; i++)
    {
      if(x == B[i])iB = i;
    }
    if(iA != -1 && iB != -1)
    {
      res *= 1;
    }

    else if(iA == -1 && iB == -1)
    {
      int cntA = 0,cntB = 0;
      // for (int i = 0; i < N; i++)
      // {
      //   if(A[i] >= x)cntA++;
      // }
      // for (int i = 0; i < M; i++)
      // {
      //   if(B[i] >= x)cntB++;
      // }
      cntA = distance(lower_bound(ALL(A),x),A.end());
      cntB = distance(lower_bound(ALL(B),x),B.end());

      res *= (cntA)*(cntB) - (N*M - x);
      
      
    }
    else
    {
      int cnt = 0;
      if(iB == -1)
      {
           cnt = distance(lower_bound(ALL(B),x),B.end());
    
        
      }
      else
      {

            cnt = distance(lower_bound(ALL(A),x),A.end());
      }
      res *= cnt;
      
    }
    

    
  }  
  cout<<res.x<<endl;
  return;
}
int32_t main(int32_t argc, const char *argv[])
{
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);

  std::cout << std::fixed;
  std::cout << std::setprecision(11);
  solve();

  return 0;
}


Measured memory_bytes: 384