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

typedef long long ll;
typedef long double ld; //
typedef double db; //
typedef string str; //
//
typedef pair<int, int> pi;
typedef pair<ll,ll> pl; //
typedef pair<ld,ld> pd; //
#define mp make_pair
#define f first
#define s second

typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<ll> vl; //
typedef vector<ld> vd; //
typedef vector<str> vs; //
typedef vector<pi> vpi; //
typedef vector<pl> vpl; //
typedef vector<pd> vpd; //
typedef vector<vi> vvi;
typedef vector<vl> vvll;

//
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() //
#define rsz resize
#define ins insert //
#define ft front() //
#define bk back() //
#define pf push_front //
#define pb push_back
#define eb emplace_back //
#define lb lower_bound //
#define ub upper_bound //

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353; // = (119<<23)+1
const int MX = 2e5+5; //
const ll INF = 1e18; //
const ld PI = 4*atan((ld)1); 
const int xd[4] = {0,1,0,-1}, yd[4] = {1,0,-1,0}; //

template<class T> bool ckmin(T& a, const T& b) { 
    return a > b ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
    return a < b ? a = b, 1 : 0; }
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());


namespace input {
	template<class T> void re(complex<T>& x);
	template<class T1, class T2> void re(pair<T1,T2>& p);
	template<class T> void re(vector<T>& a);
	template<class T, size_t SZ> void re(array<T,SZ>& a);

	template<class T> void re(T& x) { cin >> x; }
	void re(double& x) { string t; re(t); x = stod(t); }
	void re(ld& x) { string t; re(t); x = stold(t); }
	template<class T, class... Ts> void re(T& t, Ts&... ts) { 
		re(t); re(ts...); 
	}

	template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
	template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
	template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
	template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}

using namespace input;

namespace output {
	void pr(int x) { cout << x; }
	void pr(long x) { cout << x; }
	void pr(ll x) { cout << x; }
	void pr(unsigned x) { cout << x; }
	void pr(unsigned long x) { cout << x; }
	void pr(unsigned long long x) { cout << x; }
	void pr(float x) { cout << x; }
	void pr(double x) { cout << x; }
	void pr(ld x) { cout << x; }
	void pr(char x) { cout << x; }
	void pr(const char* x) { cout << x; }
	void pr(const string& x) { cout << x; }
	void pr(bool x) { pr(x ? "true" : "false"); }
	template<class T> void pr(const complex<T>& x) { cout << x; }
	
	template<class T1, class T2> void pr(const pair<T1,T2>& x);
	template<class T> void pr(const T& x);
	
	template<class T, class... Ts> void pr(const T& t, const Ts&... ts) { 
		pr(t); pr(ts...); 
	}
	template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
		pr("{",x.f,", ",x.s,"}"); 
	}
	template<class T> void pr(const T& x) { 
		pr("{"); // const iterator needed for vector<bool>
		bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; 
		pr("}");
	}
	
	void ps() { pr("\n"); } // print w/ spaces
	template<class T, class... Ts> void ps(const T& t, const Ts&... ts) { 
		pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); 
	}
	
	void pc() { pr("]\n"); } // debug w/ commas
	template<class T, class... Ts> void pc(const T& t, const Ts&... ts) { 
		pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); 
	}
	#define dbg(x...) pr("[",#x,"] = ["), pc(x);
}

using namespace output;

namespace io {
	void setIn(string s) { freopen(s.c_str(),"r",stdin); }
	void setOut(string s) { freopen(s.c_str(),"w",stdout); }
	void setIO(string s = "") {
		ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
		// cin.exceptions(cin.failbit); // ex. throws exception when you try to read letter into int
		if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
	}
}

using namespace io;

struct mi {
	typedef decay<decltype(MOD)>::type T;
	T val; 
	explicit operator T() const { return val; }
	mi() { val = 0; }
	mi(ll v) { 
		val = (-MOD <= v && v <= MOD) ? v : v % MOD;
		if (val < 0) val += MOD;
	}
	friend bool operator==(const mi& a, const mi& b) { 
		return a.val == b.val; }
	friend bool operator!=(const mi& a, const mi& b) { 
		return !(a == b); }
	friend bool operator<(const mi& a, const mi& b) { 
		return a.val < b.val; }
	friend void re(mi& a) { ll x; re(x); a = mi(x); }
	friend void pr(const mi& a) { pr(a.val); }
	friend ostream& operator<<(ostream& os, const mi& a) { 
		return os << a.val; }
   
	mi operator-() const { return mi(-val); }
	mi& operator+=(const mi& m) { 
		if ((val += m.val) >= MOD) val -= MOD; 
		return *this; }
	mi& operator-=(const mi& m) { 
		if ((val -= m.val) < 0) val += MOD; 
		return *this; }
	mi& operator++() { return *this += 1; }
	mi& operator--() { return *this -= 1; }
	friend mi operator+(mi a, const mi& b) { return a += b; }
	friend mi operator-(mi a, const mi& b) { return a -= b; }

	mi& operator*=(const mi& m) { 
		val = (ll)val*m.val%MOD; return *this; }
	friend mi pow(mi a, ll p) {
		mi ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans;
	}
	friend mi inv(const mi& a) { 
		assert(!(a == 0)); return pow(a,MOD-2); }
	mi& operator/=(const mi& m) { return (*this) *= inv(m); }
	friend mi operator*(mi a, const mi& b) { return a *= b; }
	friend mi operator/(mi a, const mi& b) { return a /= b; }
};
typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);

    int N, M;
    cin >> N >> M;

    vi A(N);
    vi B(M);
    for (int i=0;i<N;i++) cin >> A[i];
    for (int j=0;j<M;j++) cin >> B[j];

    vi rows(N*M+1, -1);
    vi cols(N*M+1, -1);

    for (int i=0;i<N;i++) {
        rows[A[i]] = i;
    }
    for (int j=0;j<M;j++) {
        cols[B[j]] = j;
    }

    vb usedrows(N, false);
    vb usedcols(M, false);

    int hnum = 0;
    int hrows = 0;
    int hcols = 0;
    
    mi ans = 1;

    for (int x=N*M; x>0; x--) {
        // cout << x << endl;
        if (rows[x] == -1 && cols[x] == -1) {
            // cout << "case 1 " << endl;
            int hiding = hrows*hcols - hnum;
            ans *= hiding;
            hnum++;
        } else if (rows[x] == -1) {
            // cout << "case 2 " << endl;
            if (usedcols[cols[x]]) {
                cout << 0 << endl;
                return 0;
            }
            ans *= hrows;

            usedcols[cols[x]] = true;
            hcols++;
            hnum++;
        } else if (cols[x] == -1) {
            // cout << "case 3 " << endl;
            if (usedrows[rows[x]]) {
                cout << 0 << endl;
                return 0;
            }
            ans *= hcols;

            usedrows[rows[x]] = true;
            hrows++;
            hnum++;
        } else {
            // cout << "case 4 " << endl;
            if (usedrows[rows[x]] || usedcols[cols[x]]) {
                cout << 0 << endl;
                return 0;
            }

            usedrows[rows[x]] = true;
            usedcols[cols[x]] = true;

            hrows++;
            hcols++;
            hnum++;
        }
    }

    cout << ans << endl;
}

Measured memory_bytes: 8064