/*** Template Begin ***/

#pragma region template

#define USING_NAMESPACE

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

typedef int64_t i64;
typedef uint64_t u64;

auto init_ = [] {
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed;
    return 0;
}();

template <typename T>
inline void in(T &x) {
    std::cin >> x;
}

template <typename T, typename... Ts>
inline void in(T &t, Ts &... ts) {
    std::cin >> t;
    in(ts...);
}

template <typename T, typename U = std::vector<T>>
inline U vin(int n) {
    U v(n);
    for (int i = 0; i < n; ++i) {
        std::cin >> v[i];
    }
    return v;
}

template <typename T, typename U = std::vector<T>, typename V = std::vector<U>>
inline V vin(int h, int w) {
    V vv(h, U(w));
    for (int i = 0; i < h; ++i) {
        for (int j = 0; j < w; ++j) {
            std::cin >> vv[i][j];
        }
    }
    return vv;
}

template <typename T>
inline void out(const T &x) {
    std::cout << x << std::endl;
}

template <char delimiter = ' ', typename T, typename... Ts>
inline void out(const T &t, const Ts &... ts) {
    std::cout << t << delimiter;
    out(ts...);
}

template <char delimiter = ' ', typename T>
inline void vout(const T &v, int n) {
    for (int i = 0; i < n; ++i) {
        if (i) std::cout << delimiter;
        std::cout << v[i];
    }
    std::cout << std::endl;
}

template <char delimiter = ' ', typename T>
inline void vout(const T &v, int h, int w) {
    for (int i = 0; i < h; ++i) {
        for (int j = 0; j < w; ++j) {
            if (j) std::cout << delimiter;
            std::cout << v[i][j];
        }
        std::cout << std::endl;
    }
}

template <typename T, size_t D>
struct multi_vector_type {
    using type = std::vector<typename multi_vector_type<T, D - 1>::type>;
};

template <typename T>
struct multi_vector_type<T, 1> {
    using type = std::vector<T>;
};

template <typename T>
struct multi_vector_type<T, 0> {
    using type = T;
};

template <typename T, size_t D>
using multi_vector = typename multi_vector_type<T, D>::type;

template <typename T, size_t D, class = typename std::enable_if<D == 0>::type>
T make_vector(const T &val = T()) {
    return val;
}

template <typename T, size_t D = 1, typename... Ts,
          class = typename std::enable_if<D != 0>::type>
multi_vector<T, D> make_vector(size_t n, Ts &&... args) {
    return multi_vector<T, D>(n, make_vector<T, D - 1>(args...));
}

namespace detail {

template <typename F>
struct Debug {
    const char *delim_ = "\n";
    F fun;

    Debug(F f) : fun(f) {}

    ~Debug() { fun(delim_); }

    Debug &delim(const char *d) {
        delim_ = d;
        return *this;
    }
};

std::deque<std::string> split(const std::string &s, char c) {
    std::deque<std::string> v;
    std::stringstream ss(s);
    std::string x;
    while (std::getline(ss, x, c)) v.emplace_back(x);
    return v;
}

template <typename T>
void deb(const char *delim, std::deque<std::string> v, T a) {
    std::cerr << v[0].substr(v[0][0] == ' ', v[0].length()) << " = " << a
              << '\n';
    std::cerr << std::flush;
}

template <typename T, typename... Args>
void deb(const char *delim, std::deque<std::string> v, T a, Args... args) {
    std::cerr << v[0].substr(v[0][0] == ' ', v[0].length()) << " = " << a
              << delim;
    v.pop_front();
    deb(delim, std::move(v), args...);
}

template <typename... Args>
auto wrap(std::deque<std::string> v, Args... args) {
    auto f = [=](const char *delim = "\n") { deb(delim, v, args...); };

    return Debug<decltype(f)>(f);
}
}

#define debug(args...) ::detail::wrap(::detail::split(#args, ','), args)

#ifdef USING_BOOST

#include <boost/math/common_factor.hpp>
#include <boost/range.hpp>
#include <boost/range/adaptors.hpp>
#include <boost/range/algorithm.hpp>
#include <boost/range/algorithm_ext.hpp>
#include <boost/range/irange.hpp>
#include <boost/range/numeric.hpp>

inline auto rep(int begin, int end) {
    if (begin > end) {
        return boost::irange(0, 0);
    } else {
        return boost::irange(begin, end);
    }
}

inline auto rep(int begin, int end, int step) {
    if ((step > 0 && begin > end) || (step < 0 && begin < end)) {
        return boost::irange(0, 0, step);
    } else {
        return boost::irange(begin, end, step);
    }
}

#endif

#ifdef USING_NAMESPACE
using namespace std;

#ifdef USING_BOOST
using namespace boost;
using namespace boost::adaptors;
#endif
#endif

#pragma endregion

/*** Template End ***/

int main() {
    int n, m;
    in(n, m);

    auto a = vin<int>(n);
    auto b = vin<int>(m);

    vector<vector<int>> x(n, vector<int>(m));

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            x[i][j] = min(a[i], b[j]);

            if (a[i] == b[j]) {
                x[i][j] *= -1;
            }
        }
    }

    vector<int> cnt1(n * m + 1);
    vector<int> cnt2(n * m + 1);

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            if (x[i][j] > 0) {
                cnt1[x[i][j]]++;
            } else {
                cnt2[-x[i][j]]++;
            }
        }
    }


    i64 ans = 1;
    const i64 mod = 1000000000 + 7;

    vector<i64> inv(n * m + 1);
    vector<i64> fact(n * m + 1);
    vector<i64> fact_inv(n * m + 1);

    for (i64 i = 1; i < n * m + 1; i++) {
        inv[i] = (i == 1) ? 1 : (mod - (mod / i) * inv[mod % i] % mod);
    }

    fact[0] = 1;
    fact_inv[0] = 1;

    for(int i = 1; i < n * m + 1; ++i) {
        fact[i] = fact[i - 1] * i % mod;
        fact_inv[i] = fact_inv[i - 1] * inv[i] % mod;
    }

    auto comb = [&](int n, int k) {
        if (n < k) {
            return i64(0);
        }

        return fact[n] * fact_inv[n - k] % mod * fact_inv[k] % mod;
    };

    int s = 0;

    for (int i = 1; i <= n * m; i++) {
        if (cnt1[i] == 0 && cnt2[i] == 0) {
            continue;
        }

        if (cnt2[i] > 1) {
            ans = 0;
            break;
        } else if (cnt2[i] == 1) {
            ans = ans * fact[cnt1[i]] % mod * comb(i - 1 - s, cnt1[i]) % mod;
        } else {
            ans = ans * fact[cnt1[i]] % mod * comb(i - 1 - s, cnt1[i] - 1) % mod;
        }

        s += cnt1[i] + cnt2[i];
    }

    out(ans);
}

Measured memory_bytes: 35456