#include "bits/stdc++.h"
// Begin Header {{{
#define all(x)          (x).begin(), (x).end()
#define rep(i, n)       for (i64 i = 0, i##_limit = (n); i < i##_limit; ++i)
#define reps(i, s, t)   for (i64 i = (s), i##_limit = (t); i <= i##_limit; ++i)
#define repr(i, s, t)   for (i64 i = (s), i##_limit = (t); i >= i##_limit; --i)
#ifndef DBG
#define trace(...)
#endif
using namespace std;
using i64 = int_fast64_t;
using pii = pair<i64, i64>;
template <class T, class U> inline bool chmax(T &a, const U &b) { return b > a && (a = b, true); }
template <class T, class U> inline bool chmin(T &a, const U &b) { return b < a && (a = b, true); }
constexpr int INF  = 0x3f3f3f3f;
constexpr i64 LINF = 0x3f3f3f3f3f3f3f3fLL;

template <class T>
inline vector<T> make_v(const T &initValue, size_t sz) {
    return vector<T>(sz, initValue);
}

template <class T, class... Args>
inline auto make_v(const T &initValue, size_t sz, Args... args) {
    return vector<decltype(make_v<T>(initValue, args...))>(sz, make_v<T>(initValue, args...));
}

inline void read() {}

template <class Head, class... Tail>
inline void read(Head &head, Tail&... tail) { cin >> head; read(tail...); }

inline void print() { cout << "\n"; }

template <class Head, class... Tail>
inline void print(Head &&head, Tail&&... tail) {
    cout << head;
    if (sizeof...(tail)) cout << ' ';
    print(forward<Tail>(tail)...);
}

template <class T>
inline ostream& operator<< (ostream &out, const vector<T> &vec) {
    static constexpr const char *delim[] = { " ", "" };
    for (const auto &e : vec) out << e << delim[&e == &vec.back()];
    return out;
}
// }}} End Header

// ModInt {{{
template<int64_t MOD>
class ModInt {
    int64_t value;
public:
    // constructor
    inline ModInt(int64_t val = 0) noexcept :
        value((val >= MOD) ? (val % MOD) : (val < 0) ? ((val + MOD) % MOD) : val) {}

    // プリミティブ整数型へのキャスト (型の明示:必要)
    template<class Int>
        explicit inline operator Int() const noexcept { return static_cast<Int>(value); }

    inline ModInt inv() const noexcept {
        return ModInt<MOD>::pow(value, MOD-2);
    }

    inline ModInt& operator+=(ModInt x) noexcept {
        if ((value += x.value) >= MOD) value -= MOD;
        return *this;
    }
    inline ModInt& operator-=(ModInt x) noexcept {
        if ((value -= x.value) < 0) value += MOD;
        return *this;
    }
    inline ModInt& operator*=(ModInt x) noexcept {
        value = (value * x.value) % MOD; return *this;
    }
    inline ModInt& operator/=(ModInt x) noexcept {
        value = (value * x.inv().value) % MOD; return *this;
    }

    inline ModInt operator+(ModInt x) const noexcept { return ModInt(*this) += x; }
    inline ModInt operator-(ModInt x) const noexcept { return ModInt(*this) -= x; }
    inline ModInt operator*(ModInt x) const noexcept { return ModInt(*this) *= x; }
    inline ModInt operator/(ModInt x) const noexcept { return ModInt(*this) /= x; }
    inline bool operator==(ModInt x) const noexcept { return value == x.value; }
    inline bool operator!=(ModInt x) const noexcept { return !(this->operator==(x)); }

    friend ostream& operator<<(ostream &os, ModInt x) noexcept { os << x.value; return os; }
    friend istream& operator>>(istream &is, ModInt &x) noexcept { is >> x.value; x.value %= MOD; return is; }

    static constexpr inline ModInt pow(int64_t n, int64_t p) noexcept {
        int64_t ret = 1;
        for(; p > 0; p >>= 1) {
            if (p & 1) ret = (ret * n) % MOD;
            n = (n * n) % MOD;
        }
        return ret;
    }
};
// }}}

constexpr int MOD = int(1e9) + 7;
using modint = ModInt<MOD>;

bool is_distinct(vector<i64> a) {
    reps(i, 1, a.size()) {
        if (a[i] == a[i-1]) return false;
    }
    return true;
}

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

    i64 H, W;
    read(H, W);

    vector<i64> row(H);
    vector<i64> col(W);

    rep(i, H) read(row[i]);
    rep(i, W) read(col[i]);
    sort(all(row));
    sort(all(col));

    if (!is_distinct(row) || !is_distinct(col)) {
        print(0);
        return 0;
    }

    modint ans = 1;
    repr(n, H*W, 1) {
        const bool exists_row = binary_search(all(row), n);
        const bool exists_col = binary_search(all(col), n);

        if (exists_row && exists_col) {
            ans *= 1;
        } else if (exists_row) {
            const i64 cnt = col.end() - upper_bound(all(col), n);
            ans *= cnt;
        } else if (exists_col) {
            const i64 cnt = row.end() - upper_bound(all(row), n);
            ans *= cnt;
        } else {
            const i64 w = col.end() - upper_bound(all(col), n);
            const i64 h = row.end() - upper_bound(all(row), n);
            ans *= (h * w) - (H * W - n);
        }
    }

    print(ans);

    return 0;
}


Measured memory_bytes: 384