double landscape.cpp

#include <cstdio>
#include <algorithm>
#define repi(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,a) repi(i,0,a)
#define all(a) (a).begin(), (a).end()

using ll = long long;
constexpr ll mod = 10000007;

ll N, M;
ll A[1010], B[1010];

int main()
{
  scanf( "%lld%lld", &N, &M );
  rep( i, N )
    scanf( "%lld", A+i );
  rep( i, M )
    scanf( "%lld", B+i );
  
  std::sort( A, A+N );
  std::sort( B, B+M );

  ll prod = 1;

  for( ll i = N*M; i > 0; --i )
  {
    ll p = std::lower_bound( A, A+N, i )-A;
    ll q = std::lower_bound( B, B+M, i )-B;

    if( A[p] == i && B[q] == i )
    {
      if( (p+1 < N && A[p+1] == A[p]) || (q+1 < M && B[q+1] == B[q]) )
        prod = 0;
    }
    else if( A[p] == i )
      prod = (prod*((M-q)-(N*M-i))) % mod;
    else if( B[q] == i )
      prod = (prod*((N-p)-(N*M-i))) % mod;
    else
      prod = (prod*((N-p)*(M-q)-(N*M-i))) % mod;
  }

  printf( "%lld\n", prod );

  return 0;
}