#include <cassert>
#include <cstdio>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <numeric>
#include <algorithm>

using namespace std;
using lint = long long;
constexpr int MOD = 1000000007, INF = 1010101010;
constexpr lint LINF = 1LL << 60;

template <class T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
	for (const auto &e : vec) os << e << (&e == &vec.back() ? "\n" : " ");
	return os;
}

#ifdef _DEBUG
template <class T>
void dump(const char* str, T &&h) { cerr << str << " = " << h << "\n"; };
template <class Head, class... Tail>
void dump(const char* str, Head &&h, Tail &&... t) {
	while (*str != ',') cerr << *str++; cerr << " = " << h << "\n";
	dump(str + (*(str + 1) == ' ' ? 2 : 1), t...);
}
#define DMP(...) dump(#__VA_ARGS__, __VA_ARGS__)
#else 
#define DMP(...) ((void)0)
#endif

template<int Modulo = MOD>
struct Mint {

	lint val;
	constexpr Mint(lint v = 0) noexcept : val(v % Modulo) { if (val < 0) val += Modulo; }

	constexpr Mint& operator += (const Mint &r) noexcept {
		val += r.val;
		if (val >= Modulo) val -= Modulo;
		return *this;
	}
	constexpr Mint& operator -= (const Mint &r) noexcept {
		val -= r.val;
		if (val < 0) val += Modulo;
		return *this;
	}
	constexpr Mint& operator *= (const Mint &r) noexcept {
		val = val * r.val % Modulo;
		return *this;
	}
	constexpr Mint& operator /= (const Mint &r) noexcept {
		lint a = r.val, b = Modulo, u = 1, v = 0;
		while (b) {
			lint t = a / b;
			a -= t * b; swap(a, b);
			u -= t * v; swap(u, v);
		}
		val = val * u % Modulo;
		if (val < 0) val += Modulo;
		return *this;
	}

	constexpr Mint operator + (const Mint &r) const noexcept { return Mint(*this) += r; }
	constexpr Mint operator - (const Mint &r) const noexcept { return Mint(*this) -= r; }
	constexpr Mint operator * (const Mint &r) const noexcept { return Mint(*this) *= r; }
	constexpr Mint operator / (const Mint &r) const noexcept { return Mint(*this) /= r; }

	constexpr int getmod() { return Modulo; }
	constexpr Mint operator - () const noexcept { return val ? Modulo - val : 0; }

	constexpr bool operator == (const Mint &r) const noexcept { return val == r.val; }
	constexpr bool operator != (const Mint &r) const noexcept { return val != r.val; }

	friend ostream &operator << (ostream &os, const Mint<Modulo> &x) noexcept { return os << x.val; }
	friend istream &operator >> (istream &is, Mint<Modulo> &x) noexcept {
		lint tmp; is >> tmp;
		x = Mint<Modulo>(tmp);
		return is;
	}
	friend constexpr Mint<Modulo> modpow(const Mint<Modulo> &a, lint n) noexcept {
		Mint res(1), tmp = a;
		while (n > 0) {
			if (n & 1) res *= tmp;
			tmp *= tmp;
			n >>= 1;
		}
		return res;
	}
};

using mint = Mint<>;

class Factorial {
private:
	vector<lint> fac, inv, finv;

	void build(int N) {
		fac[0] = fac[1] = 1; inv[1] = 1; finv[0] = finv[1] = 1;

		for (int i = 2; i < N; 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;
		}
	}

public:
	Factorial(int N = 110000) : fac(N + 1), inv(N + 1), finv(N + 1) { build(N + 1); }

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

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

int main() {

	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	int N, M;
	cin >>N>>M;
	vector<int> A(N), B(M);
	for (int i = 0; i < N; i++) cin >> A[i];
	for (int i = 0; i < M; i++) cin >> B[i];
	sort(A.begin(), A.end());
	sort(B.begin(), B.end());

	mint ans = 1;
	for (int i = 0; i < N - 1; i++) if (A[i + 1] == A[i]) ans = 0;
	for (int i = 0; i < M - 1; i++) if (B[i + 1] == B[i]) ans = 0;

	Factorial Fac(1000000);
	int row = 0, col = 0;
	int cnt = 0, prev = 0;
	while (row < N && col < M) {

		if (A[row] < B[col]) {
			cnt += A[row] - prev - 1;
			prev = A[row];
			ans *= M - col;
			ans *= Fac.Pmod(cnt, M - col - 1);
			cnt -= M - col - 1;
			row++;
		}
		else if (A[row] > B[col]){
			cnt += B[col] - prev - 1;
			prev = B[col];
			ans *= N - row;
			ans *= Fac.Pmod(cnt, N - row - 1);
			cnt -= N - row - 1;
			col++;
		}
		else {
			cnt += A[row] - prev - 1;
			prev = A[row];
			ans *= Fac.Pmod(cnt, N + M - (row + col) - 2);
			cnt -= N + M - (row + col) - 2;
			row++, col++;
		}

	}

	cout << ans << "\n";

	return 0;
}


Measured memory_bytes: 23808