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

#define NDEBUG
#include <cassert>


typedef long long ll;
typedef long double Double;
typedef unsigned long long ull;
typedef pair<int,int> ii;
typedef pair<ll,ll> llll;
typedef pair<double,double> dd;

typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ii> vii;
typedef vector<vector<ii>> vvii;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<llll> vllll;
typedef vector<bool> vb;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<long double> vD;

#define sz(a)  int((a).size())
#define pb  push_back
#define eb  emplace_back
#define FOR(var,from,to) for(int var=(from);var<=(to);++var)
#define rep(var,n)  for(int var=0;var<(n);++var)
#define rep1(var,n)  for(int var=1;var<=(n);++var)
#define repC2(vari,varj,n)  for(int vari=0;vari<(n)-1;++vari)for(int varj=vari+1;varj<(n);++varj)
#define repC3(vari,varj,vark,n)  for(int vari=0;vari<(n)-2;++vari)for(int varj=vari+1;varj<(n)-1;++varj)for(int vark=varj+1;vark<(n);++vark)
#define ALL(c)  (c).begin(),(c).end()
#define RALL(c)  (c).rbegin(),(c).rend()
#define tr(i,c)  for(auto i=(c).begin(); i!=(c).end(); ++i)
#define found(s,e)  ((s).find(e)!=(s).end())
#define mset(arr,val)  memset(arr,val,sizeof(arr))
#define mid(x,y) ((x)+((y)-(x))/2)
#define IN(x,a,b) ((a)<=(x)&&(x)<=(b))
#define cons make_pair

template<class T> inline void amin(T & a, T const & b) { a = min(a, b); }
template<class T> inline void amax(T & a, T const & b) { a = max(a, b); }
template<typename X, typename T> auto vectors(X x, T a) { return vector<T>(x, a); }
template<typename X, typename Y, typename Z, typename... Zs> auto vectors(X x, Y y, Z z, Zs... zs) { auto cont = vectors(y, z, zs...); return vector<decltype(cont)>(x, cont); }


ll gcd(ll a, ll b) { while(a) swap(a, b%=a); return b; }

const ll MOD=1000000007LL;

ll ADD(ll x, ll y) { return (x+y) % MOD; }
ll SUB(ll x, ll y) { return (x-y+MOD) % MOD; }
ll MUL(ll x, ll y) { return x*y % MOD; }
ll POW(ll x, ll e) { ll v=1; for(; e; x=MUL(x,x), e>>=1) if (e&1) v = MUL(v,x); return v; }
ll DIV(ll x, ll y) { /*assert(y%MOD!=0);*/ return MUL(x, POW(y, MOD-2)); }
ll comb(ll n, ll k) { ll v=1; for(ll i=1; i<=k; i++) v = DIV(MUL(v, n-i+1),i); return v; }

#define INTSPACE 12
char _buf[INTSPACE*1000000 + 3];

int loadint() {
    if (fgets(_buf, INTSPACE+3, stdin)==NULL) return 0;
    return atoi(_buf);
}

int loadvec(vector<int>& v, int N=-1) {
    if (N == 0) {
        v.clear();
        return 0;
    }
    if (N == -1) {
        N = loadint();
        if (N==0) return 0;
    }
    int bufsize = INTSPACE*N + 3;
    if (fgets(_buf, bufsize, stdin)==NULL) return 0;
    v.resize(N);

    int i=0;
    bool last = false;
    for (char *p=&_buf[0]; ;) {
        char *q = p;
        while (*q > ' ') ++q;
        if (*q == 0x0D || *q == 0x0A) last = true;
        *q = 0;
        v[i++] = atoi(p);
        if (last || i == N) break;
        p = q+1;
    }
    return i;
}
void read_cr() {
    fgets(_buf, 256, stdin);
}



ll solve(int N,int M,vi& a,vi& b) {
    set<int> sa(ALL(a)), sb(ALL(b));
    if (sa.size() < N || sb.size() < M) return 0;


    int Z = N*M;

    vll fact(Z+1);
    fact[0] = fact[1] = 1;
    for(int i=2; i<=Z; ++i) fact[i] = MUL(fact[i-1], i);

    vi visited(Z+1, 0);
    priority_queue<int,vi,greater<int>> pq;

    rep(r,N) rep(c,M) {
        if (a[r] == b[c]) {
            visited[ a[r] ] = 1;
        } else {
            int mn = min(a[r], b[c]);
            pq.push(mn);
        }
    }

    ll ans = 1;
    int cnt = 0;

    int wait = 0;
    for (int n=1; n<=Z; ++n) {
        while (!pq.empty()) {
            if (pq.top() == n) { ++cnt; pq.pop(); }
            else break;
        }

        if (!visited[n]) ++wait;
        if (cnt == 0) continue;


        if (wait < cnt) return 0;



        ll p = 1;
        if (visited[n]) {
            p = MUL(comb(wait,cnt), fact[cnt]);
        } else {
            p = MUL(comb(wait-1,cnt-1), fact[cnt]);
        }

        ans = MUL(ans, p);

        wait -= cnt; cnt = 0;

    }
    if (wait > 0) return 0;

    return ans;
}

int main() {
    int N, M; scanf("%d%d", &N, &M); read_cr();
    vi a(N), b(M);
    loadvec(a,N);
    loadvec(b,M);
    cout << solve(N,M,a,b) << endl;
    return 0;
}


Measured memory_bytes: 18032