#include <bits/stdc++.h>
using namespace std;

#define rep(i, m, n) for(int(i) = (int)(m); i < (int)(n); ++i)
#define rep2(i, m, n) for(int(i) = (int)(n)-1; i >= (int)(m); --i)
#define REP(i, n) rep(i, 0, n)
#define REP2(i, n) rep2(i, 0, n)
#define all(hoge) (hoge).begin(), (hoge).end()
#define en '\n'
using ll = long long;
using ull = unsigned long long;
template <class T>
using vec = vector<T>;
template <class T>
using vvec = vector<vec<T>>;
typedef pair<ll, ll> P;
constexpr long long INF = 1LL << 60;
constexpr int INF_INT = 1 << 25;
constexpr long long MOD = (ll)1e9 + 7;
//constexpr long long MOD = 998244353LL;
using ld = long double;
static const ld pi = 3.141592653589793L;
typedef vector<ll> Array;
typedef vector<Array> Matrix;

template <class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

struct Edge {
    ll to, rev;
    long double cap;
    Edge(ll _to, long double _cap, ll _rev) {
        to = _to;
        cap = _cap;
        rev = _rev;
    }
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;

void add_edge(Graph &G, ll from, ll to, long double cap, bool revFlag,
              long double revCap) {
    G[from].push_back(Edge(to, cap, (ll)G[to].size()));
    if(revFlag)
        G[to].push_back(Edge(from, revCap, (ll)G[from].size() - 1));
}

template <int mod>
struct ModInt {
    int x;

    ModInt() : x(0) {}

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod)
            x -= mod;
        return *this;
    }

    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod)
            x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }

    ModInt operator-() const { return ModInt(-x); }

    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

    bool operator==(const ModInt &p) const { return x == p.x; }

    bool operator!=(const ModInt &p) const { return x != p.x; }

    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }

    ModInt pow(int64_t n) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
            if(n & 1)
                ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p) {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, ModInt &a) {
        int64_t t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }

    static int get_mod() { return mod; }
};

using mint = ModInt<MOD>;

// 二項係数ライブラリ
template <class T>
struct Combination {
    vector<T> fact_, inv_, finv_;
    constexpr Combination() {}
    constexpr Combination(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n + 1);
    }
    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].get_mod();
        for(int i = 2; i < n; i++) {
            fact_[i] = fact_[i - 1] * i;
            inv_[i] = -inv_[MOD % i] * (MOD / i);
            finv_[i] = finv_[i - 1] * inv_[i];
        }
    }
    constexpr T nPr(int n, int k) const noexcept {
        if(n < k || n < 0 || k < 0)
            return 0;
        return fact_[n] * finv_[n - k];
    }
    constexpr T nCr(int n, int k) const noexcept {
        if(n < k || n < 0 || k < 0)
            return 0;
        return fact_[n] * finv_[k] * finv_[n - k];
    }
    constexpr T nHr(int n, int k) const noexcept {
        if(n < k || n < 0 || k < 0)
            return 0;
        return nCr(n + k - 1, k);
    }
    constexpr T fact(int n) const noexcept {
        if(n < 0)
            return 0;
        return fact_[n]; //n!
    }
    constexpr T inv(int n) const noexcept {
        if(n < 0)
            return 0;
        return inv_[n]; //1/n
    }
    constexpr T finv(int n) const noexcept {
        if(n < 0)
            return 0;
        return finv_[n]; //1/n!
    }
};

void solve() {
    ll n, m;
    cin >> n >> m;
    vec<ll> a(n), b(m);
    REP(i, n) { cin >> a[i]; }
    REP(i, m) { cin >> b[i]; }
    sort(all(a));
    sort(all(b));

    REP(i, n - 1) {
        if(a[i] == a[i + 1]) {
            cout << 0 << en;
            return;
        }
    }
    REP(i, m - 1) {
        if(b[i] == b[i + 1]) {
            cout << 0 << en;
            return;
        }
    }

    if(a[n - 1] != b[m - 1] or a[n - 1] != n * m) {
        cout << 0 << en;
        return;
    }

    Combination<mint> com(n * m);

    mint ans = 1;
    ll used = 0;
    vec<bool> flag(m, false);

    int i = 0, j = 0;
    while(used < n * m) {
        if(a[i] < b[j]) {
            ans *= com.nPr(a[i] - used - 1, m - j - 1) * (m - j);
            i++;
            used += m - j;
        } else if(a[i] == b[j]) {
            ans *= com.nPr(a[i] - used - 1, m - j - 1);
            flag[j] = true;
            i++;
            used += m - j;
        } else {
            if(flag[j])
                ans *= com.nPr(b[j] - used, n - i);
            else
                ans *= com.nPr(b[j] - used - 1, n - i - 1) * (n - i);
            j++;
            used += n - i;
        }
    }
    cout << ans << en;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    solve();
    /*
    ll t;
    cin >> t;
    REP(i, t)
    solve();
    */

    return 0;
}


Measured memory_bytes: 18744