#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using VI = vector<int>;
using VL = vector<ll>;
using VS = vector<string>;
template<class T> using PQ = priority_queue<T, vector<T>, greater<T>>;
#define FOR(i,a,n) for(int (i)=(a);(i)<(n);++(i))
#define eFOR(i,a,n) for(int (i)=(a);(i)<=(n);++(i))
#define rFOR(i,a,n) for(int (i)=(n)-1;(i)>=(a);--(i))
#define erFOR(i,a,n) for(int (i)=(n);(i)>=(a);--(i))
#define each(i, a) for(auto &i : a)
#define SORT(i) sort((i).begin(),(i).end())
#define rSORT(i,a) sort((i).begin(),(i).end(),(a))
#define all(i) (i).begin(),(i).end()
#define out(y,x) ((y) < 0 || h <= (y) || (x) < 0 || w <= (x))
#define line cout << "-----------------------------\n" 
#define ENDL(i,n) ((i) == (n) - 1 ? "\n" : " ")
#define stop system("pause")
constexpr ll INF = 1000000000;
constexpr ll LLINF = 1LL << 60;
constexpr ll mod = 1000000007;
constexpr ll MOD = 998244353;
constexpr ld eps = 1e-10;
constexpr ld pi = 3.1415926535897932;
template<class T>inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T>inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; }return false; }
inline void init() { cin.tie(nullptr); cout.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); }
template<class T>inline istream& operator>>(istream& is, vector<T>& v) { for (auto& elemnt : v)is >> elemnt; return is; }
template<class T>inline istream& operator>>(istream& is, deque<T>& v) { for (auto& elemnt : v)is >> elemnt; return is; }
template<class T, class U>inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template<class T>inline vector<T> vec(size_t a) { return vector<T>(a); }
template<class T>inline vector<T> defvec(T def, size_t a) { return vector<T>(a, def); }
template<class T, class... Ts>inline auto vec(size_t a, Ts... ts) { return vector<decltype(vec<T>(ts...))>(a, vec<T>(ts...)); }
template<class T, class... Ts>inline auto defvec(T def, size_t a, Ts... ts) { return vector<decltype(defvec<T>(def, ts...))>(a, defvec<T>(def, ts...)); }

int main() {
    init();

    int h, w; cin >> h >> w;
    VI a(h + 1), b(w + 1);
    FOR(i, 0, h)cin >> a[i];
    FOR(i, 0, w)cin >> b[i];

    rSORT(a, greater<int>()), rSORT(b, greater<int>());
    bool ng = a[0] != b[0] || min(a[h - 1], b[w - 1]) == 1;
    FOR(i, 1, h)ng |= a[i - 1] == a[i];
    FOR(i, 1, w)ng |= b[i - 1] == b[i];

    int y = 1, x = 1, bef = a[0], cand = 0;
    ll ans = (ng ? 0 : 1);
    while (y < h || x < w) {
        if (a[y] == b[x]) {
            for (--bef; b[x] < bef; --bef, --cand) {
                ans = ans * cand % mod;
            }
            cand += y++ + x++;
        }
        else {
            VI *A = &a, *B = &b;
            int *Y = &y, *X = &x;

            if (a[y] < b[x]) {
                swap(A, B), swap(Y, X);
            }
            for (--bef; (*A)[*Y] < bef; --bef, --cand) {
                ans = ans * cand % mod;
            }
            ans = ans * *X % mod;
            cand += *X - 1;
            ++*Y;
        }
    }

    for (; 0 < cand; --cand)ans = ans * cand % mod;

    cout << ans << "\n";
}

Measured memory_bytes: 256