#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int,int> pii;
typedef pair<int,ll> pil;
typedef pair<ll,int> pli;
typedef pair<ll,ll> pll;

template<class T,class U>constexpr bool chmin(T&a,const U b){if(a<=b)return false;a=b;return true;}
template<class T,class U>constexpr bool chmax(T&a,const U b){if(a>=b)return false;a=b;return true;}
#define bit(n,k) ( (n>>k)&1 )

//デバッグ
template<class T>
void Vout(vector<T> &V){
    cout<<"\nstart\n";
    const int sz=V.size();
    for(int i=0;i<sz;i++){
        cout<<i<<" "<<V[i]<<'\n';
    }
    cout<<"end\n"<<endl;
}

template<class T>
void VPout(vector<T> &V){
    cout<<"\nstart\n";
    const int sz=V.size();
    for(int i=0;i<sz;i++){
        cout<<i<<" "<<V[i].first<<" "<<V[i].second<<'\n';
    }
    cout<<"end\n"<<endl;
}


//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


constexpr int MAX=1<<30;
constexpr ll INF=1LL<<62;
constexpr int MOD=1e9+7;
int dx[]={1,-1,0,0},dy[]={0,0,-1,1};

//__builtin_popcount(S);
//#define int ll
//vector<vector<int>> data(3, vector<int>(4));
//vector.resize(a,vector<int>(b,-1));
//vector<vector<vector<要素の型>>> 変数名(要素数1, vector<vector<要素の型>>(要素数2, vector<要素の型>(要素数3, 初期値)));

struct ModInt{
    ll a;
    constexpr ModInt() :a(0){}
    constexpr ModInt(ll x) :a((x>=0)?(x%MOD):(x%MOD+MOD) ) {}

    constexpr ModInt operator+(const ModInt rhs)const noexcept{
        return ModInt(*this)+=rhs;
    }
    constexpr ModInt operator-(const ModInt rhs)const noexcept{
        return ModInt(*this)-=rhs;
    }
    constexpr ModInt operator*(const ModInt rhs)const noexcept{
        return ModInt(*this)*=rhs;
    }
    constexpr ModInt operator/(const ModInt rhs)const noexcept{
        return ModInt(*this)/=rhs;
    }
    constexpr ModInt &operator+=(const ModInt rhs)noexcept{
        a+=rhs.a;
        if(a>=MOD) a-=MOD;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt rhs)noexcept{
        a-=rhs.a;
        if(a<0) a+=MOD;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt rhs)noexcept{
        a=(a*rhs.a)%MOD;
        return *this;
    }
    constexpr ModInt &operator/=(ModInt rhs)noexcept{
        a=(a*rhs.inverse().a)%MOD;
        return *this;
    }

    constexpr ModInt operator=(ll x)noexcept{
        x%=MOD;
        if(x<0) x+=MOD;
        a=x;
        return *this;
    }

    constexpr bool operator==(const ModInt p)const noexcept{
        return a==p.a;
    }

    constexpr bool operator!=(const ModInt p)const noexcept{
        return a!=p.a;
    }

    constexpr ModInt pow(ll N) const noexcept{
        ModInt ans(1LL),p(a);
        while(N>0){
            if(bit(N,0)){
                ans*=p;
            }
            p*=p;
            N>>=1;
        }
        return ans;
    }
    constexpr ModInt inverse() const noexcept{
        return pow(MOD-2);
    }

};

constexpr ModInt Mr(ll p){
    p%=MOD;
    if(p<0) p+=MOD;
    return ModInt(p);
}



signed main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr); 

    int N,M;
    cin>>N>>M;
    vector<int> A(N),B(M);
    for(int i=0;i<N;i++) cin>>A[i];
    for(int i=0;i<M;i++) cin>>B[i];
    A.push_back(-1);
    B.push_back(-1);
    sort(A.rbegin(),A.rend());
    sort(B.rbegin(),B.rend());
    if( !(A[0]==N*M && B[0]==N*M) ){
        cout<<0<<endl;
        return 0;
    }
    int nowA=0,nowB=0;
    int count=1;
    ModInt ans(1);
    for(int i=N*M-1;i>=1;i--,count++){
        if(i<A[nowA+1] || i<B[nowB+1]){
            cout<<0<<endl;
            return 0;
        }
        if(A[nowA+1]==i && B[nowB+1]==i){
            nowA++; nowB++;
        }else if(A[nowA+1]==i){
            nowA++;
            ans*=Mr(nowB+1);
        }else if(B[nowB+1]==i){
            nowB++;
            ans*=Mr(nowA+1);
        }else{
            if( (nowA+1)*(nowB+1)<=count ){
                cout<<0<<endl;
                return 0;
            }
            ans*=Mr((nowA+1)*(nowB+1)-count);
        }
    }
    cout<<ans.a<<endl;
}

Measured memory_bytes: 256