#include <iostream>
#include <algorithm>
#include <vector>
#include <string.h>
#include <queue>
using namespace std;
#define mod (long)(1e9 + 7)
#define all(x) (x).begin(), (x).end()
#define bitcount(n) __builtin_popcountl(long(n))
#define fcout cout << fixed << setprecision(15)
#define highest(x) (63 - __builtin_clzl(x))
//#define long long long
template<class T> inline void YES(T condition){ if(condition) cout << "YES" << endl; else cout << "NO" << endl; }
template<class T> inline void Yes(T condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
template<class T> inline void POSS(T condition){ if(condition) cout << "POSSIBLE" << endl; else cout << "IMPOSSIBLE" << endl; }
template<class T> inline void Poss(T condition){ if(condition) cout << "Possible" << endl; else cout << "Impossible" << endl; }
template<class T> inline void First(T condition){ if(condition) cout << "First" << endl; else cout << "Second" << endl; }
template<class T = string, class U = char>int character_count(T text, U character){ int ans = 0; for(U i: text){ ans += (i == character); } return ans; }
long power(long base, long exponent, long module){ if(exponent % 2){ return power(base, exponent - 1, module) * base % module; }else if(exponent){ long root_ans = power(base, exponent / 2, module); return root_ans * root_ans % module; }else{ return 1; }}
struct position{ int y, x; }; position mv[4] = {{-1, 0}, {0, 1}, {1, 0}, {0, -1}}; // double euclidean(position first, position second){ return sqrt((second.x - first.x) * (second.x - first.x) + (second.y - first.y) * (second.y - first.y)); }
template<class T, class U> string to_string(pair<T, U> x){ return to_string(x.first) + "," + to_string(x.second); }
template<class itr> void array_output(itr start, itr goal){ string ans; for(auto i = start; i != goal; i++){ ans += to_string(*i) + " "; } ans.pop_back(); cout << ans << endl; }
template<class itr> void cins(itr start, itr goal){ for(auto i = start; i != goal; i++){ cin >> (*i); } }
template<class T> T gcd(T a, T b){ if(a && b){ return gcd(min(a, b), max(a, b) % min(a, b)); }else{ return a; }} template<class T> T lcm(T a, T b){ return a / gcd(a, b) * b; }
struct combination{ vector<long> fact, inv; combination(int sz) : fact(sz + 1), inv(sz + 1){ fact[0] = 1; for(int i = 1; i <= sz; i++){ fact[i] = fact[i - 1] * i % mod; } inv[sz] = power(fact[sz], mod - 2, mod); for(int i = sz - 1; i >= 0; i--){ inv[i] = inv[i + 1] * (i + 1) % mod; } } long C(int p, int q) const{ if(q < 0 || p < q) return 0; return (fact[p] * inv[q] % mod * inv[p - q] % mod); } };

combination table(3e6);

int main(){
    long N, M;
    cin >> N >> M;
    long A[N], B[M];
    cins(A, A + N);
    sort(A, A + N);
    cins(B, B + M);
    sort(B, B + M);
    if(A[N - 1] < N * M || B[M - 1] < N * M){
        cout << 0 << endl;
        return 0;
    }
    long maximum[N][M];
    for(int i = 0; i < N; i++){
        for(int j = 0; j < M; j++){
            maximum[i][j] = min(A[i], B[j]);
        }
    }
    long ans = 1;
    vector<bool> is_in_remaining(N * M, true);
    for(int i = 0; i < N; i++){
        long count = 0;
        is_in_remaining[A[i] - 1] = false;
        for(int j = 0; j < M; j++){
            if(A[i] == B[j]){
                maximum[i][j] = -1;
                goto next;
            }
            count += (A[i] < B[j]);
        }
        maximum[i][M - 1] = -1;
        ans = (ans * count) % mod;
    next:;
    }
    for(int i = 0; i < M; i++){
        long count = 0;
        is_in_remaining[B[i] - 1] = false;
        for(int j = 0; j < N; j++){
            if(B[i] == A[j]){
                goto next2;
            }
            count += (B[i] < A[j]);
        }
        maximum[N - 1][i] = -1;
        ans = (ans * count) % mod;
    next2:;
    }
    vector<long> out_edge;
    for(int i = 0; i < N; i++){
        for(int j = 0; j < M; j++){
            if(maximum[i][j] != -1){
                out_edge.push_back(maximum[i][j] - 1);
            }
        }
    }
    sort(all(out_edge));
    vector<long> lower;
    for(int i = 0; i < N * M; i++){
        if(is_in_remaining[i]){
            lower.push_back(i);
        }
    }
    for(int i = 0; i < lower.size(); i++){
        long times = (upper_bound(all(lower), out_edge[i]) - lower.begin() - i);
        if(times <= 0){
            cout << 0 << endl;
            return 0;
        }
        ans = ans * times % mod;
    }
    cout << ans % mod << endl;
}


Measured memory_bytes: 77544