#include "bits/stdc++.h"
// Begin Header {{{
#define all(x) (x).begin(), (x).end()
#define rep(i, s, n) for (i64 i = (s), i##_limit = (n); i < i##_limit; ++i)
#define repr(i, s, t) for (i64 i = (s), i##_limit = (t); i >= i##_limit; --i)
#define var(type, ...) \
    type __VA_ARGS__;  \
    read(__VA_ARGS__);
#ifndef DBG
#define dump(...)
#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> makeV(const T &initValue, size_t sz) {
    return vector<T>(sz, initValue);
}

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

template <class T>
inline istream &operator>>(istream &is, vector<T> &vec) {
    for (auto &e : vec) is >> e;
    return is;
}

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 &os, const vector<T> &vec) {
    static constexpr const char *delim[] = {" ", ""};
    for (const auto &e : vec) os << e << delim[&e == &vec.back()];
    return os;
}

template <class Container>
struct Rev {
    Container &x_;
    inline Rev(Container &x) : x_(x) {}
    inline auto begin() { return rbegin(x_); }
    inline auto end() { return rend(x_); }
};
// }}} End Header

constexpr int MOD = int(1e9) + 7;

// ModInt {{{
template <int64_t MOD>
class ModInt {
    int64_t value;

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

    template <class IntegerType>
    explicit inline operator IntegerType() const noexcept {
        return static_cast<IntegerType>(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;
    }

    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;
    }
};
// }}}
using modint = ModInt<MOD>;

// Factorial, InvFact {{{
template <size_t N, int MOD>
struct Factorial {
    uint_fast64_t f[N + 1];

    inline Factorial() : f{1} {
        for (int i = 1; i <= N; ++i) f[i] = (f[i - 1] * i) % MOD;
    }

    constexpr inline ModInt<MOD> operator[](size_t i) const { return f[i]; }
};

template <size_t N, int MOD>
struct InvFact {
    uint_fast64_t inv[N + 1];
    uint_fast64_t f[N + 1];

    inline InvFact() : inv{0, 1}, f{1, 1} {
        for (int i = 2; i <= N; ++i) {
            inv[i] = (MOD - MOD / i) * inv[MOD % i] % MOD;
            f[i] = f[i - 1] * inv[i] % MOD;
        }
    }

    constexpr inline ModInt<MOD> operator[](size_t i) const { return f[i]; }
};
// }}}
Factorial<200010, MOD> fact;
InvFact<200010, MOD> invFact;
ModInt<MOD> nCr(int n, int r) {
    return (r < 0 || n < r) ? 0 : (fact[n] * (invFact[r] * invFact[n - r]));
}
ModInt<MOD> nPr(int n, int r) {
    return (r < 0 || n < r) ? 0 : (fact[n] * invFact[n - r]);
}
ModInt<MOD> nHr(int n, int r) { return nCr(n + r - 1, r); }

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

    var(int, H, W);
    vector<int> row(H), col(W);
    read(row, col);
    sort(all(row));
    sort(all(col));

    {
        vector<int> x(row);
        row.erase(unique(all(row)), row.end());
        if (row.size() != H) {
            print(0);
            return 0;
        }
    }
    {
        vector<int> x(col);
        col.erase(unique(all(col)), col.end());
        if (col.size() != W) {
            print(0);
            return 0;
        }
    }

    modint ans = 1;
    int cnt = 0;
    repr(n, H * W, 1) {
        auto rowItr = lower_bound(all(row), n);
        auto colItr = lower_bound(all(col), n);
        if (rowItr == end(row) || colItr == end(col)) {
            ans = 0;
            break;
        }

        const int h = end(row) - lower_bound(all(row), n);
        const int w = end(col) - lower_bound(all(col), n);

        if (*rowItr == n && *colItr == n) {
            ans *= 1;
        } else if (*rowItr == n) {
            ans *= w;
        } else if (*colItr == n) {
            ans *= h;
        } else {
            ans *= h * w - cnt;
        }

        ++cnt;
    }

    print(ans);

    return 0;
}


Measured memory_bytes: 4992