#include <bits/stdc++.h>

using namespace std;

#define pb push_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define endl "\n"

#define aim_cpo do{ios::sync_with_stdio(false);\
cin.tie(nullptr);cout.precision(10);cout<<fixed;}while(0)

#define LOCAL_INPUT do{FILE *stream1;\
stream1=freopen("/Users/aim_cpo/CLionProjects/competitive/in.txt","r",stdin);\
if(stream1==nullptr)return 0;}while(0)
#define LOCAL_OUTPUT do{FILE *stream2;\
stream2 = freopen("out.txt", "w", stdout);\
if (stream2 == nullptr) return 0;}while(0)

#ifdef LOCAL_DEFINE
#define show(x) cerr << #x << " = " << (x) << endl
#define showV(v, n) do{\
for(int _i_t_e_=0; _i_t_e_<(n);_i_t_e_++)\
cerr<<"("<<_i_t_e_<<" = "<<(v)[_i_t_e_]<<") ";\
cerr<<endl;}while(0);
#define showA(a, n) do{\
for(int _i_t_e_=0;_i_t_e_<(n);_i_t_e_++)\
cerr<<"("<<_i_t_e_<<" = "<<(a)[_i_t_e_]<<") ";\
cerr<<endl;}while(0);
#else
#define show(x)
#define showV(v, n)
#define showA(a, n)
#endif

typedef long long ll;
typedef unsigned long long ull;

constexpr const int INT_INF=0x3f3f3f3f; //1061109567
constexpr const ll LL_INF=0x3f3f3f3f3f3f3f3f; //4557430888798830399

template <typename T> bool chmin(T &a, T b){return a>b?(a=b,true):false;}
template <typename T> bool chmax(T &a, T b){return a<b?(a=b,true):false;}

// INT
#define GCD(a, b) __gcd(a, b)
template <typename T> T LCM(T a, T b) {return a / GCD(a, b) * b;}
template <typename T> T EXTGCD(T a, T b, T& x, T& y) {
    T d = a;
    if (b != 0) {d=EXTGCD(b,a%b,y,x);y-=(a/b)*x;}
    else x=1,y=0;
    return d;
}
template <typename T> bool is_prime(T a) {
    for(int i=2;i*i<=a;i++)if(a%i==0)return 1;
    return 0;
}

// MOD
ll MOD = 1000000000L + 7L;
#define add(a, b) ((a % MOD) + (b % MOD)) % MOD
#define mul(a, b) ((a % MOD) * (b % MOD)) % MOD
#define sub(a, b) ((a % MOD) + MOD - (b % MOD)) % MOD
template <typename T> T mod_inverse(T a, T mod, bool prime){ // if mod is prime, "prime" is true.
    if(prime){
        T tmp=mod-2,now=a,res=1;while(tmp){if(tmp&1)res=mul(res,now);now=mul(now,now);tmp>>=1;}
        return res;
    }else{T x,y;EXTGCD(a,mod,x,y);return (mod+x%mod)%mod;}
}
#define divide(a, b) ((a % MOD) * (mod_inverse(b, MOD, true))) % MOD

//LLの数値をつかう時は最後にLをつける癖をつけよう
//
//  ┏┓┏┓　┓　┏┓
//  ┏┛┃┃　┃　┗┫
//  ┗┛┗┛　┻　┗┛
//
//   謹┃賀┃新┃年┃
//   ━┛━┛━┛━┛
//WWWWWWWWWWWWWWWWWWWWWW

int n, m;
int a[1011], b[1011];
int idx1[1000001], idx2[1000001];
int _min[1011][1011];
int cont[1000011];
set<int> set1, set2;

int main() {
    aim_cpo; // インタラクティブのときは消すように.
#ifdef LOCAL_DEFINE
    LOCAL_INPUT; // インタラクティブのときは消すように.
//    LOCAL_OUTPUT; // ファイルに出力したいときのみ
    show(MOD);
#endif
    cin >> n >> m;
    for (int i = 0; i < 1000001; i++) {
        idx1[i] = -1, idx2[i] = -1;
    }
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        idx1[a[i]] = i;
        set1.insert(a[i]);
    }
    for (int i = 0; i < m; i++) {
        cin >> b[i];
        idx2[b[i]] = i;
        set2.insert(b[i]);
    }
    if ((int)set1.size() != n) {
        cout << 0 << endl;
        return 0;
    }
    if ((int)set2.size() != m) {
        cout << 0 << endl;
        return 0;
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            _min[i][j] = min(a[i], b[j]);
            cont[_min[i][j]]++;
        }
    }
    ll ans = 1L;
    int nokori = 0;
    for (int i = n * m; i >= 1; i--) {
        if (idx1[i] != -1 && idx2[i] != -1) {
            nokori += cont[i] - 1;
            continue;
        }
        if (cont[i] > 0) {
            ans = mul(ans, cont[i]);
            nokori += cont[i] - 1;
        } else {
            if (nokori > 0) {
                ans = mul(ans, nokori);
                nokori--;
            } else {
                ans = 0;
                break;
            }
        }
        show(ans);
        show(nokori);
    }
    cout << ans << endl;
#ifdef  LOCAL_DEFINE
    cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << "s." << endl;
#endif
    return 0;
}

Measured memory_bytes: 14080