#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <limits>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <functional>
#include <iomanip>

using namespace std;

#ifdef LOCAL
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define eprintf(...) 42
#endif
using ll = long long;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
using vvvll = std::vector<vvll>;
#define reps(i, S, E) for (ll i = (S); i <= (E); i++)
#define rep(i, N) reps(i, 0, N-1)
#define deps(i, E, S) for (ll i = (E); i >= (S); i--)
#define dep(i, N) deps(i, N-1, 0)
const ll INF = 1LL << 60;
const int INF_INT = 1 << 30;

template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
struct mll {
	static ll MOD;
	ll val;
	mll(ll v = 0) : val(v % MOD) { if (val < 0) val += MOD; }
	mll operator - () const { return -val; }
	mll operator + (const mll &b) const { return val + b.val; }
	mll operator - (const mll &b) const { return val - b.val; }
	mll operator * (const mll &b) const { return val * b.val; }
	mll operator / (const mll &b) const { return mll(*this) /= b; }
	mll operator + (ll b) const { return *this + mll(b); }
	mll operator - (ll b) const { return *this - mll(b); }
	mll operator * (ll b) const { return *this * mll(b); }
	friend mll operator + (ll a, const mll &b) { return b + a; }
	friend mll operator - (ll a, const mll &b) { return -b + a; }
	friend mll operator * (ll a, const mll &b) { return b * a; }
	mll &operator += (const mll &b) { val = (val + b.val) % MOD; return *this; }
	mll &operator -= (const mll &b) { val = (val + MOD - b.val) % MOD; return *this; }
	mll &operator *= (const mll &b) { val = (val*b.val) % MOD; return *this; }
	mll &operator /= (const mll &b) {
		ll c = b.val, d = MOD, u = 1, v = 0;
		while (d) {
			ll t = c / d;
			c -= t * d; swap(c, d);
			u -= t * v; swap(u, v);
		}
		val = val * u % MOD;
		if (val < 0) val += MOD;
		return *this;
	}
	mll &operator += (ll b) { return *this += mll(b); }
	mll &operator -= (ll b) { return *this -= mll(b); }
	mll &operator *= (ll b) { return *this *= mll(b); }
	mll &operator /= (ll b) { return *this /= mll(b); }
	bool operator == (const mll &b) { return val == b.val; }
	bool operator != (const mll &b) { return val != b.val; }
	bool operator == (ll b) { return *this == mll(b); }
	bool operator != (ll b) { return *this != mll(b); }
	friend bool operator == (ll a, const mll &b) { return mll(a) == b.val; }
	friend bool operator != (ll a, const mll &b) { return mll(a) != b.val; }
	friend ostream &operator << (ostream &os, const mll &a) { return os << a.val; }
	friend istream &operator >> (istream &is, mll &a) { return is >> a.val; }
	static mll Combination(ll a, ll b) {
		chmin(b, a - b);
		if (b < 0) return mll(0);
		mll c = 1;
		rep(i, b) c *= a - i;
		rep(i, b) c /= i + 1;
		return c;
	}
};
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;

struct Fast {
	Fast() {
		cin.tie(0);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
	}
} fast; //cin,cout高速化のおまじない＋桁数指定

ll mll::MOD = (ll)(1e9 + 7);// 998244353ll;

//--debug--
#ifdef LOCAL
void _debug_out_(string s = "") {
	if (s != "") { eprintf(s.c_str()); } else { eprintf("\n"); }
}
void _debug_out_(ll x, string s = "") {
	if (s != "") { eprintf(s.c_str(), x); }	else { eprintf("%lld\n", x); }
}
void _debug_out_(mll x, string s = "") {
	if (s != "") { eprintf(s.c_str(), x); }
	else { eprintf("%lld\n", x.val); }
}
void _debug_out_(vvll x, string s = "") {
	string t = s;
	if (s == "") {
		ll maxLen = 0;
		rep(i, (ll)x.size()) rep(j, (ll)x[i].size()) {
			ll n = x[i][j] / 10, len = 1;
			while (n > 0) { len++; n /= 10; }
			chmax(maxLen, len);
		}
		t = "%" + to_string(maxLen) + "lld ";
	}
	rep(i, (ll)x.size()) { rep(j, (ll)x[i].size()) { eprintf(t.c_str(), x[i][j]); } eprintf("\n"); }
	eprintf("\n");
}
void _debug_out_(vll x, string s = "") {
	rep(i, (ll)x.size()) { if (s != "") { eprintf(s.c_str(), x[i]); } else { eprintf("%lld ", x[i]); } }
	eprintf("\n");
}
void _debug_out_(vector<bool> x) {
	rep(i, (ll)x.size()) { eprintf("%s", x[i] ? "o" : "x");	}
	eprintf("\n");
}
void _debug_out_(vector<vector<bool>> x) {
	rep(i, (ll)x.size()) { rep(j, (ll)x[i].size()) { eprintf("%s", x[i][j] ? "o" : "x"); } eprintf("\n"); }
	eprintf("\n");
}
void _debug_out_(map<ll, ll> x) {
	auto begin = x.begin(), end = x.end();
	for (auto iter = begin; iter != end; iter++) { eprintf("%lld:%lld ", iter->first, iter->second); }
	eprintf("\n");
}
void _debug_out_(map<char, ll> x) {
	auto begin = x.begin(), end = x.end();
	for (auto iter = begin; iter != end; iter++) { eprintf("%c:%lld ", iter->first, iter->second); }
	eprintf("\n");
}
#define debug_out(...) _debug_out_(__VA_ARGS__)
#else
#define debug_out(...) 42
#endif
//--debug--


//◆--↓--階乗をmodした数値を高速に求める--↓--
const ll MAX = 2000000;
const ll MOD = 1000000007;
ll fac[MAX];

//テーブルを作る前処理
void FACinit() {
	fac[0] = fac[1] = 1;
	for (ll i = 2; i < MAX; i++) {
		fac[i] = fac[i - 1] * i % MOD;
	}
}

//階乗計算
mll FAC(ll n) {
	return fac[n];
}
//--↑--階乗をmodした数値を高速に求める--↑--


struct LLTriple {
	ll num = 0;
	ll rowFlag = 0;
	ll index = 0;
	ll fixed = 0;
	LLTriple() {}
	LLTriple(ll num, ll rowFlag, ll index, ll fixed) {
		this->num = num;
		this->rowFlag = rowFlag;
		this->index = index;
		this->fixed = fixed;
	}
};

int main() {
	ll R;
	cin >> R;
	ll C;
	cin >> C;

	set<ll> sR;
	vector<ll> r(R);
	rep(i, R) {
		cin >> r[i];
		if (sR.count(r[i]) > 0) {
			//多重に入っているのでダメ
			cout << 0 << endl;
			return 0;
 		}
		sR.insert(r[i]);
	}
	set<ll> sC;
	vector<ll> c(C);
	rep(i, C) {
		cin >> c[i];
		if (sC.count(c[i]) > 0) {
			//多重に入っているのでダメ
			cout << 0 << endl;
			return 0;
		}
		sC.insert(c[i]);
	}

	//全行列の数をソートする
	vector<LLTriple> A;
	rep(i, R) {
		A.push_back(LLTriple(r[i], 1, i, (sC.count(r[i]) > 0 ? 1 : 0)));
	}
	rep(i, C) {
		A.push_back(LLTriple(c[i], 0, i, (sR.count(c[i]) > 0 ? 1 : 0)));
	}
	std::sort(A.begin(), A.end(), [](const LLTriple &a, const LLTriple &b) {
		return a.num < b.num; //降順にするには > とする
	});


	mll result = 1;
	ll usedCount = 0;
	ll rowIndex = 0;
	ll colIndex = 0;
	FACinit();
	set<ll> sFixedNum;

	rep(i, R + C) {
		debug_out();
		debug_out("i:");
		debug_out(i);
		debug_out("num:");
		debug_out(A[i].num);
		debug_out("row?:");
		debug_out(A[i].rowFlag);
		debug_out("fixed?:");
		debug_out(A[i].fixed);

		mll pat = 1;

		//詰めることができる残りセル数
		ll nCell = A[i].rowFlag ? C - colIndex : R - rowIndex;

		//詰めることができる数の個数
		ll nNum = A[i].num - usedCount;

		//位置固定の場合
		bool fix = false;

		if (sFixedNum.count(A[i].num) > 0) { //sFixedNumにすでに入っている場合は固定済み
			//固定済みなのでセル数も詰めることができる数の個数もそのまま
		}
		else if (A[i].fixed) { 
			nCell--;
			nNum--;
			sFixedNum.insert(A[i].num);
			fix = true;
		}
		else {
			//numがどこかに入り、残りのセルを詰める
			pat *= nCell;
			nCell--;
			nNum--;
			fix = true;
		}
		
		debug_out("nCell:");
		debug_out(nCell);
		debug_out("nNum:");
		debug_out(nNum);

		//詰める場合の数
		pat *= FAC(nNum) / FAC(nNum - nCell);
		result *= pat;

		debug_out("pat:");
		debug_out(pat);
		debug_out("result:");
		debug_out(result);

		//詰めた数のカウント
		usedCount += nCell + (fix ? 1 : 0);

		//行列index進める
		if (A[i].rowFlag) {
			rowIndex++;
		}
		else {
			colIndex++;
		}
	}

	cout << result << endl;

	return 0;
}

Measured memory_bytes: 16128