#include <bits/stdc++.h>
#include <sys/types.h>
#include <unistd.h>

#define _overload(_1,_2,_3,name,...) name
#define _rep(i,n) _range(i,0,n)
#define _range(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload(__VA_ARGS__,_range,_rep,)(__VA_ARGS__)

#define _rrep(i,n) _rrange(i,n,0)
#define _rrange(i,a,b) for(int i=int(a)-1;i>=int(b);--i)
#define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__)

#define _all(arg) begin(arg),end(arg)
#define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg))
#define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary)
#define clr(a,b) memset((a),(b),sizeof(a))
#define bit(n) (1LL<<(n))
#define popcount(n) (__builtin_popcountll(n))

using namespace std;

template<class T>bool chmax(T &a, const T &b) { return (a<b)?(a=b,1):0;}
template<class T>bool chmin(T &a, const T &b) { return (b<a)?(a=b,1):0;}

using ll=long long;
using R=long double;
const R EPS=1e-9L; // [-1000,1000]->EPS=1e-8 [-10000,10000]->EPS=1e-7
inline int sgn(const R& r){return(r > EPS)-(r < -EPS);}
inline R sq(R x){return sqrt(max(x,0.0L));}

const int dx[8]={1,0,-1,0,1,-1,-1,1};
const int dy[8]={0,1,0,-1,1,1,-1,-1};

const pid_t pid = getpid();
// Problem Specific Parameter:

template<unsigned MOD>  class ModInt {
public:
	ModInt(): x(0) {}
	ModInt(signed y) : x(y >= 0 ? y % MOD : MOD - (-y) % MOD) {}
	ModInt(signed long long y) : x(y >= 0 ? y % MOD : MOD - (-y) % MOD) {}


	// Arithmetic Oprators
	ModInt &operator+=(ModInt that) {
		if ((x += that.x) >= MOD) x -= MOD; 
		return *this;
	}
	ModInt &operator-=(ModInt that) {
		if ((x += MOD - that.x) >= MOD) x -= MOD; 
		return *this;
	}
	ModInt &operator*=(ModInt that) {
		x = 1LL * x * that.x % MOD;
		return *this;
	}
	ModInt &operator/=(ModInt that) {
		return *this *= ModInt(get<1>(extgcd(that.x, int(MOD))));
	}
	ModInt &operator%=(ModInt that) {
		x %= that.x;
		return *this;
	}

	ModInt &operator+=(const int that) { return *this += ModInt(that);}
	ModInt &operator-=(const int that) { return *this -= ModInt(that);}
	ModInt &operator*=(const int that) { return *this *= ModInt(that);}
	ModInt &operator/=(const int that) { return *this /= ModInt(that);}
	ModInt &operator%=(const int that) { return *this %= ModInt(that);}

	// Comparators
	bool operator <(ModInt that) { return x < that.x; }
	bool operator >(ModInt that) { return x > that.x; }
	bool operator<=(ModInt that) { return x <= that.x; }
	bool operator>=(ModInt that) { return x >= that.x; }
	bool operator!=(ModInt that) { return x != that.x; }
	bool operator==(ModInt that) { return x == that.x; }

	// Utilities
	unsigned getval() const { return x;}
	ModInt operator+(ModInt that) const { return ModInt(*this) += that;}
	ModInt operator-(ModInt that) const { return ModInt(*this) -= that;}
	ModInt operator*(ModInt that) const { return ModInt(*this) *= that;}
	ModInt operator/(ModInt that) const { return ModInt(*this) /= that;}
	ModInt operator%(ModInt that) const { return ModInt(*this) %= that;}
	ModInt operator+(const int that) const { return ModInt(*this) += that;}
	ModInt operator-(const int that) const { return ModInt(*this) -= that;}
	ModInt operator*(const int that) const { return ModInt(*this) *= that;}
	ModInt operator/(const int that) const { return ModInt(*this) /= that;}
	ModInt operator%(const int that) const { return ModInt(*this) %= that;}
	ModInt operator=(const int that) { return *this = ModInt(that);}
	friend istream &operator>>(istream& is, ModInt &that) {ll tmp; is >> tmp; that = ModInt(tmp);return is;}
	friend ostream &operator<<(ostream& os, const ModInt &that) { return os << that.x; }
	
	ModInt power(ll n) const {
		ll b = 1LL, a = x;
		while(n){
			if(n & 1) b = b * a % MOD;
			a = a * a % MOD;
			n >>= 1;
		}
		return ModInt(b);
	}
private:
	unsigned x;
	
	inline auto extgcd(int a, int b) {
		if (b == 0) return make_tuple(a, 1, 0);
		tuple<int, int, int> ret = extgcd(b, a % b);
		swap(get<1>(ret), get<2>(ret));
		get<2>(ret) -= a / b * get<1>(ret);
		return ret;
	}
};

const int mod = 1000000007;
using mint = ModInt<mod>;
const mint ZERO = mint(0);
const mint ONE = mint(1);


vector<mint> Fact, InvFact;
void makeFact(int n){
	Fact = vector<mint>(n+1);
	Fact[0] = mint(1);
	rep(i,1,n+1) Fact[i] = mint(i) * Fact[i-1];

	InvFact = vector<mint>(n+1);
	InvFact[n] = mint(1) / Fact[n];
	rrep(i,n) InvFact[i] = mint(i+1) * InvFact[i+1];
}

mint Factorial(int n){ return Fact[n];}
mint InverseFactorial(int n){ return InvFact[n];}
mint Permutation(int n,int k){ return (n < 0 or k < 0 or n - k < 0) ? ZERO : Fact[n] * InvFact[n - k];}
mint Combination(int n,int k){ return (n < 0 or k < 0 or n - k < 0) ? ZERO : Fact[n] * InvFact[k] * InvFact[n-k];}

const int limit = 1000010;
int a[1010],b[1010];

int elem[limit];
int same[limit];

int main(void){
	int n,m;
	cin >> n >> m;
	rep(i,n) cin >> a[i];
	rep(j,m) cin >> b[j];

	rep(i,n)rep(j,m){
		if(a[i] == b[j]) same[a[i]]++;
		elem[min(a[i],b[j])]++;
	}

	int cur = 0;
	makeFact(n * m);

	mint ans = ONE;

	rep(i,1,n*m+1){
		const int k = elem[i];
		cur++;

		if(k == 0) continue;

		if(same[i] >= 2){
			ans = ZERO;
			break;
		}

		
		if(same[i]){
			ans *= Permutation(cur - 1, k - 1); 
		} else {
			ans *= mint(k) * Permutation(cur - 1, k - 1);
		}

		cur -= elem[i];
	}

	cout << ans << endl;
	return 0;
}

Measured memory_bytes: 10112