#include <bits/stdc++.h>
using namespace std;
const long long MOD=1e9+7;

template<uint_fast64_t Modulus> class modint{
    using u64=uint_fast64_t;
    public:
    u64 a;
    constexpr modint(const u64 x=0) noexcept:a(((x%Modulus)+Modulus)%Modulus){}
    constexpr u64 &value() noexcept{return a;}
    constexpr const u64 &value() const noexcept{return a;}
    constexpr modint &operator+=(const modint &rhs) noexcept{
        a+=rhs.a;
        if (a>=Modulus) a-=Modulus;
        return *this;
    }
    constexpr modint operator+(const modint &rhs) const noexcept{
        return modint(*this)+=rhs;
    }
    constexpr modint &operator++() noexcept{
        return ++a,*this;
    }
    constexpr modint operator++(int) noexcept{
        modint t=*this; return ++a,t;
    }
    constexpr modint &operator-=(const modint &rhs) noexcept{
        if (a<rhs.a) a+=Modulus;
        a-=rhs.a;
        return *this;
    }
    constexpr modint operator-(const modint &rhs) const noexcept{
        return modint(*this)-=rhs;
    }
    constexpr modint &operator--() noexcept{
        return --a,*this;
    }
    constexpr modint operator--(int) noexcept{
        modint t=*this; return --a,t;
    }
    constexpr modint &operator*=(const modint &rhs) noexcept{
        a=a*rhs.a%Modulus;
        return *this;
    }
    constexpr modint operator*(const modint &rhs) const noexcept{
        return modint(*this)*=rhs;
    }
    constexpr modint &operator/=(modint rhs) noexcept{
        u64 exp=Modulus-2;
        while(exp){
            if (exp&1) *this*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return *this;
    }
    constexpr modint operator/(const modint &rhs) const noexcept{
        return modint(*this)/=rhs;
    }
    constexpr modint operator-() const noexcept{
        return modint(Modulus-a);
    }
    constexpr bool operator==(const modint &rhs) const noexcept{
        return a==rhs.a;
    }
    constexpr bool operator!=(const modint &rhs) const noexcept{
        return a!=rhs.a;
    }
    constexpr bool operator!() const noexcept{return !a;}
    friend constexpr modint pow(modint rhs,long long exp) noexcept{
        modint res{1};
        while(exp){
            if (exp&1) res*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return res;
    }
    template<class T> friend constexpr modint operator+(T x,modint y) noexcept{
        return modint(x)+y;
    }
    template<class T> friend constexpr modint operator-(T x,modint y) noexcept{
        return modint(x)-y;
    }
    template<class T> friend constexpr modint operator*(T x,modint y) noexcept{
        return modint(x)*y;
    }
    template<class T> friend constexpr modint operator/(T x,modint y) noexcept{
        return modint(x)/y;
    }
    friend ostream &operator<<(ostream &s,const modint &rhs) noexcept{
        return s << rhs.a;
    }
    friend istream &operator>>(istream &s,modint &rhs) noexcept{
        u64 a; rhs=modint{(s >> a,a)}; return s;
    }
};

using mint=modint<MOD>;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    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];
    sort(A.begin(),A.end()); reverse(A.begin(),A.end());
    sort(B.begin(),B.end()); reverse(B.begin(),B.end());
    for (int i=0;i<N-1;++i) if (A[i]==A[i+1]){
        cout << 0 << '\n'; return 0;
    }
    for (int i=0;i<M-1;++i) if (B[i]==B[i+1]){
        cout << 0 << '\n'; return 0;
    }
    if (A[0]!=N*M||B[0]!=N*M){
        cout << 0 << '\n'; return 0;
    }
    mint ans=1;
    int nowa=0,nowb=0;
    for (int i=N*M;i>=1;--i){
        while(nowa<N&&i<=A[nowa]) ++nowa;
        while(nowb<M&&i<=B[nowb]) ++nowb;
        if (A[nowa-1]==i&&B[nowb-1]==i) continue;
        if (A[nowa-1]==i){ans*=nowb; continue;}
        if (B[nowb-1]==i){ans*=nowa; continue;}
        ans*=nowa*nowb-(N*M-i);
    }
    cout << ans << '\n';
}

Measured memory_bytes: 256