#include <bits/stdc++.h>
#include <iomanip>
//#define DEBUG 1

using namespace std;

typedef long long LL;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<LD, LD> PLDLD;
typedef vector<int> VI;
typedef vector<LL> VLL;
typedef vector<char> VB;

#define FOR(i,a,b) for(int i=(a);i<(int)(b);++i)
#define REP(i,n) FOR(i,0,n)
#define CLR(a) memset((a), 0 ,sizeof(a))
#define ALL(a) a.begin(),a.end()
#define UNQ(a) a.erase(std::unique(ALL(a)),a.end());
#define endl "\n"

const LD EPS=1e-5;
const long long INFLL=(LL)(1e9)*(LL)(1e9);
const int INF=1e9+7;

template<class T>
void chmin(T& a, const T b)
{
	if(a>b)
		a=b;
}
template<class T>
void chmax(T& a, const T b)
{
	if(a<b)
		a=b;
}

const LL powLL(const LL p, const LL q)
{
	LL t=1;
	for(int i=0;i<q;i++)
		t*=p;
	return t;
}

template <typename T>
struct has_iter
{
	private:
		template <typename U>
		static constexpr true_type check(typename U::iterator*);
		template <typename U>
		static constexpr false_type check(...);

	public:
		static constexpr bool value = decltype(check<T>(nullptr))::value;
};


template<typename T, typename U = typename T::iterator>
void print(const T& container)
{
		auto&& first=begin(container), last=end(container);
		auto&& back=prev(last);
		for(auto e=first; e!=last; e=next(e))
			cout<<*e<<" \n"[e==back];
}


extern void* enabler;
template<typename Head, typename enable_if<!has_iter<Head>::value>::type*& = enabler>
void print(const Head& head)
{
	cout<<head<<endl;
}

template<> void print<string>(const string& container)
{
	cout<<container<<endl;
}

template<typename Head, typename... Tail>
void print(const Head& head, const Tail&... tail)
{
	cout<<head<<" ";
	print(tail...);
}

template<typename... Args>
void printd(const Args&... args)
{
	#ifdef DEBUG
		print(args...);
	#endif
}

template<typename Head>
void input(Head& head)
{
	cin>>head;
}

template<typename Head, typename... Tail>
void input(Head& head, Tail&... tail)
{
	cin>>head;
	input(tail...);
}

void io_speedup()
{
	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(false);
}

template<typename T>
istream& operator >> (istream& is, vector<T>& vec)
{
	for(T& x: vec) is >> x;
	return is;
}


template<typename T, typename U>
istream& operator >> (istream& is, pair<T, U>& t)
{
	is>>t.first>>t.second;
	return is;
}

template<int N, typename... Ts, typename enable_if<N == sizeof...(Ts)-1>::type*& = enabler>
void tuple_in(istream &is, tuple<Ts...> &t)
{
	is>>get<N>(t);
}
template<int N, typename... Ts, typename enable_if<N < sizeof...(Ts)-1>::type*& = enabler>
void tuple_in(istream &is, tuple<Ts...> &t)
{
	is>>get<N>(t);
	tuple_in<N+1, Ts...>(is, t);
}

template<typename... Ts>
istream& operator >> (istream& is, tuple<Ts...>& t)
{
	tuple_in<0, Ts...>(is, t);
	return is;
}


template<typename T, typename U>
ostream& operator << (ostream& os, const pair<T, U>& t)
{
	os<<'('<<t.first<<", "<<t.second<<')';
	return os;
}

template<int N, typename... Ts, typename enable_if<N == sizeof...(Ts)-1>::type*& = enabler>
void tuple_out(ostream &os,const tuple<Ts...> &t)
{
	os<<get<N>(t);
}
template<int N, typename... Ts, typename enable_if<N < sizeof...(Ts)-1>::type*& = enabler>
void tuple_out(ostream &os,const tuple<Ts...> &t)
{
	os<<get<N>(t)<<", ";
	tuple_out<N+1, Ts...>(os, t);
}

template<typename... Ts>
ostream& operator << (ostream& os, const tuple<Ts...>& t)
{
	os<<'(';
	tuple_out<0, Ts...>(os, t);
	os<<')';
	return os;
}

template<typename T>
vector<T> read(int n)
{
	vector<T> t(n);
	cin>>t;
	return t;
}

template<typename T>
T read()
{
	T t;
	cin>>t;
	return t;
}

template<typename Head, typename... Tail>
struct vector_demensions
{
	using type=vector<typename vector_demensions<Tail...>::type>;
};

template<typename Head>
struct vector_demensions<Head> { using type=Head; };

template<typename T>
vector<T> make_vectors(int size, T val)
{
	return vector<T>(size, val);
}

template<typename T=int, typename... Args>
auto make_vectors(int size, Args... tail)
	-> typename vector_demensions<Args..., T>::type
{
	auto val=make_vectors<T>(forward<Args>(tail)...);
	return vector<decltype(val)>(size, val);
}

//c++14

class Mod
{
	public:
		using value_type = long long;

	private:
		static const value_type MODULO = 1e9+7;
		value_type value;

		constexpr value_type Normalize(value_type x) const
		{
			return x<0?(x%MODULO+MODULO):(x%MODULO);
		}

	public:
		constexpr Mod():value(0){}
		constexpr Mod(const value_type &val):value(Normalize(val)) {}
		
		constexpr explicit operator value_type () const
		{
			return value;
		}

		constexpr const Mod operator -() const
		{
			return Mod(MODULO - value);
		}
		constexpr const Mod operator +(const Mod &rhs) const
		{
			return Mod(value + rhs.value);
		}
		constexpr const Mod operator -(const Mod &rhs) const
		{
			return Mod(value + (-rhs).value);
		}
		constexpr const Mod operator *(const Mod &rhs) const
		{
			return Mod(value * rhs.value);
		}
		constexpr Mod &operator +=(const Mod &rhs)
		{
			value = Normalize(value + rhs.value);
			return *this;
		}
		constexpr Mod &operator -=(const Mod &rhs)
		{
			value = Normalize(value - rhs.value);
			return *this;
		}
		constexpr Mod &operator *=(const Mod &rhs)
		{
			value = Normalize(value * rhs.value);
			return *this;
		}


		constexpr Mod pow(value_type p) const;

		constexpr Mod inv() const
		{
			return pow(MODULO-2);
		}

		constexpr const Mod operator /(const Mod &rhs) const
		{
			return *this * rhs.inv();
		}
		constexpr Mod &operator /=(const Mod &rhs)
		{
			return *this = *this / rhs;
		}  
		constexpr bool operator ==(const Mod &rhs)
		{
			return value == rhs.value;
		}
};

constexpr Mod Mod::pow(value_type p) const
{
	Mod tmp=1, mult=*this;
	while(p)
	{
		if((p&1)>0) tmp*=mult;
		p>>=1;
		mult*=mult;
	}
	return tmp;
}

namespace std
{
	ostream& operator<<(ostream& os, const Mod mod)
	{
		os<<(typename Mod::value_type)mod;
		return os;
	}
};



template<size_t N>
struct Factorial
{
	private:
		Mod ary[N];
	public:
		constexpr explicit Factorial():ary()
		{
			ary[0]=1;
			for(size_t i=1;i<N;i++)
				ary[i]=ary[i-1]*i;
		}

		constexpr size_t size() const {   return N;  }

		constexpr Mod operator[] (const int id) const
		{
			return ary[id];
		}
};

template<size_t N>
class FactorialInv
{
	private:
		Mod ary[N];
	public:
		constexpr explicit FactorialInv(const Factorial<N> &fact):ary()
		{
			for(size_t i=0;i<N;i++)
				ary[i]=fact[i].inv();
		}

		//FactorialInv& operator=(FactorialInv&&)=default;

		constexpr Mod operator[] (const int id) const
		{
			return ary[id];
		}
};

template<size_t N, size_t M = N>
class Combination
{
	private:
		const Factorial<N> fact;
		const FactorialInv<M> fact_inv;
	public:
		constexpr Combination(const Factorial<N> fact_, const FactorialInv<M> fact_inv_)
		:fact(fact_),fact_inv(fact_inv_)
		{}

		constexpr Mod operator()(const int n, const int m) const
		{
			return (fact)[n] * (fact_inv)[m] * (fact_inv)[n-m];
		}
};

int main()
{
	int n,m;
	input(n,m);
	set<int> a,b;
	REP(i,n)
		a.insert(read<int>());
	REP(i,m)	
		b.insert(read<int>());
	//sort(ALL(a));
	//sort(ALL(b));
	int d=0;
	int uv=0,uh=0;
	bool f=1;
	Mod ans=1; 
	for(int i=n*m;i>0;i--)
	{
		bool ia=(a.find(i)!=a.end());
		bool ib=(b.find(i)!=b.end());
		if(ia&&ib)
		{
			d+=uv+uh;
			uv++;
			uh++;
		}
		else if(ib)
		{
			ans*=uv;
			if(uv==0) f=0;
			d+=uv-1;
			uh++;
		}
		else if(ia)
		{
			ans*=uh;
			if(uh==0) f=0;
			d+=uh-1;
			uv++;
		}
		else
		{
			ans*=d;
			if(d==0) f=0;
			d--;
		}
		if(!f)
		{
			printd(i,uv,uh,d);
			break;
		}
	}
	printd(uv,uh,d);
	if(!f)print(0);
	else print(ans);
}

Measured memory_bytes: 384