#include <bits/stdc++.h>
using namespace std;

typedef pair<int, int> pii;
typedef long long ll;
template<class T> using V = vector<T>;
template<class T> using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i,n) rep2(i,0,n)
#define rep2(i,m,n) for(int i=m;i<(n);i++)
#define ALL(c) (c).begin(),(c).end()
#define dump(x) cerr << #x << " = " << (x) << endl
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

template<class T, class U> void chmin(T& t, const U& u) { if (t > u) t = u; }
template<class T, class U> void chmax(T& t, const U& u) { if (t < u) t = u; }

template<class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
	os<<"{";
	rep(i, v.size()) {
		if (i) os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

template <unsigned int MOD>
struct ModInt {
	using uint = unsigned int;
	using ull = unsigned long long;
	using M = ModInt;

	uint v;

	ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
	M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
		v = (_v < MOD) ? _v : _v - MOD;
		return *this;
	}

	explicit operator bool() const { return v != 0; }
	M operator+(const M& a) const { return M().set_norm(v + a.v); }
	M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
	M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
	M operator/(const M& a) const { return *this * a.inv(); }
	M& operator+=(const M& a) { return *this = *this + a; }
	M& operator-=(const M& a) { return *this = *this - a; }
	M& operator*=(const M& a) { return *this = *this * a; }
	M& operator/=(const M& a) { return *this = *this / a; }
	M operator-() const { return M() - *this; }
	M& operator++(int) { return *this = *this + 1; }
	M& operator--(int) { return *this = *this - 1; }

	M pow(ll n) const {
		if (n < 0) return inv().pow(-n);
		M x = *this, res = 1;
		while (n) {
			if (n & 1) res *= x;
			x *= x;
			n >>= 1;
		}
		return res;
	}

	M inv() const {
		ll a = v, b = MOD, p = 1, q = 0, t;
		while (b != 0) {
			t = a / b;
			swap(a -= t * b, b);
			swap(p -= t * q, q);
		}
		return M(p);
	}

	bool operator==(const M& a) const { return v == a.v; }
	bool operator!=(const M& a) const { return v != a.v; }
	friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
};

using Mint = ModInt<1000000007>;

int main() {
	int N, M;
	cin >> N >> M;
	V<int> A(N), B(M);
	rep(i, N) cin >> A[i];
	rep(i, M) cin >> B[i];
	sort(ALL(A));
	sort(ALL(B));

	Mint ans(1);

	rep(i, N-1) if (A[i] == A[i+1]) {
		ans = 0;
	}
	rep(i, M-1) if (B[i] == B[i+1]) {
		ans = 0;
	}

	A.pb(TEN(9));
	B.pb(TEN(9));

	for (int i = N * M; i >= 1; --i) {
		int p = lower_bound(ALL(A), i) - A.begin();
		int q = lower_bound(ALL(B), i) - B.begin();
		if (A[p] == i && B[q] == i) {
			//do nothing;
		} else if (A[p] == i) {
			Mint x(M - q);
			ans *= x;
		} else if (B[q] == i) {
			Mint x(N - p);
			ans *= x;
		} else {
			ll v = (ll)(N - p) * (M - q) - (N * M - i);
			if (v > 0) {
				Mint x(v);
				ans *= x;
			} else {
				ans = 0;
			}
		}
	}
	cout << ans << endl;

	return 0;
}

Measured memory_bytes: 256