#ifdef LOCAL
//#define _GLIBCXX_DEBUG
#pragma comment(linker, "/STACK:102400000,102400000")
#endif
#pragma GCC optimize("Ofast") // Ofast 等效于 -O3 -ffast-math
#include <bits/stdc++.h>

using namespace std;

#define FAST_READ ios::sync_with_stdio(false); cin.tie(nullptr);
#ifdef LOCAL
#define see(x) cout  <<"<DBG> " << #x << ": " << (x) << endl
#endif
#ifndef LOCAL
#define see(x)
#endif

template<typename T> void dprintln(const T &t) { cout << t << endl; } // for debug use
template<typename T, typename ...Args> void dprintln(const T &t, const Args &...rest) { cout << t << ' '; dprintln(rest...); }
template<typename T> void println(const T &t) { cout << t << '\n'; }
template<typename T, typename ...Args> void println(const T &t, const Args &...rest) { cout << t << ' '; println(rest...); }

template<typename T> void print(const T &t) { cout << t << ' '; }

template<typename T, typename ...Args> void print(const T &t, const Args &...rest) { cout << t << ' '; print(rest...); }

// this overload is chosen when there's only one argument
template<class T> void scan(T &t) { cin >> t; }
template<class T, class ...Args> void scan(T &a, Args &...rest) { cin >> a; scan(rest...); }
template <typename T> void read(vector<T> &vec) {for(auto &x: vec) cin >> x;}
using ll = long long;
using vl = vector<ll>;
using vi = vector<int>;
using pii = pair<int,int>;
using vb = vector<bool>;
using vpii = vector<pii>;

#define rng(i, a, b) for(int i = (a); i < (b); ++i)
#define down(i, b, a) for (int i = (b); i >= (a); i--)
#define rep(n) for(int _ = 0, __ = (int)n; _ < __; _++)
#define stp(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(x, cont) for (const auto &x: cont)
#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define SZ(x) (int)(x).size()
#define pq(T,COMP) priority_queue<T, vector<T>, COMP>
#define popcnt(x) __builtin_popcount((x))
#define SET(arr, v) memset(arr, (v), sizeof (arr))
#define UNIQ(vec) (vec).erase(unique(all(vec)), end(vec))
#define LB(cont, x) int(lower_bound(all(cont), x) - begin(cont))
#define AI(name, n, m) vv<int> name(n, vi(m));
#define AL(name, n, m) vv<ll> name(size_t(n), vl(size_t(m)));
auto bet = [](const ll x, const ll y, const ll i) {
    return x <= i && i <= y;
};

template<typename T1, typename T2>
T1 ceil(T1 x, T2 y) { // y >= 1，是整数。需要注意 x + y - 1 是否会溢出
    return (x + y - 1) / y;
}


inline int h_bit(unsigned long long x) {
    return sizeof(unsigned long long) * 8 - 1 - __builtin_clzll(x);
}

template <typename T>
struct bit {
    vector<T> a;
    explicit bit(int n, int v = 0) {
        a.resize(n + 1);
        if(v != 0) {
            for (int i = 1; i <= n; ++i) a[i] = v;
        }
    }

    T sum(T x) {
        T res = 0;
        while (x) {
            res += a[x];
            x -= x & -x;
        }
        return res;
    }

    T sum(int l, int r) {
        if (l > r) return 0;
        return sum(r) - sum(l - 1);
    }

    void add(int x, T v) {
        while (x < a.size()) {
            a[x] += v;
            x += x & -x;
        }
    }
    void clear(){
        fill(a.begin(), a.end(), 0);
    }
};
vi get_prime(int n) {
    vi minp(n + 1), p;
    for (int i = 2; i <= n; i++) {
        if (!minp[i]) {
            minp[i] = i;
            p.pb(i);
        }
        FOR(x, p) {
            if (x <= minp[i] && x * i <= n)
                minp[x * i] = x;
            else break;
        }
    }
    return p;
}

const int mod = 1e9+7; //记住 mod 的行号！

inline void add_mod(ll &x, const ll y) {
    x += y;
    if (x >= mod) x -= mod;
}

inline ll submod(ll x, ll y) {
    return x >= y ? x - y : x - y + mod;
}
inline ll addmod(ll x, ll y) {
    x += y;
    return x >= mod ? x - mod : x;
}

inline void sub_mod(ll &x, const ll y) {
    x -= y;
    if (x < 0) x += mod;
}
// alias templates
template<typename T> using vv = vector<vector<T>>;
template <typename T1, typename T2 = T1> using vp = vector<pair<T1,T2>>;
template<typename T, int n> using va = vector<array<T,n>>;

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

template <typename T>
using rank_tree = __gnu_pbds::tree<
        T,
        __gnu_pbds::null_type,
        less<T>,
        __gnu_pbds::rb_tree_tag,
        __gnu_pbds::tree_order_statistics_node_update>;


//union-find 并查集
struct UF{
    vi par, sz;
    int tot;
    explicit UF(int n) { //0-indexed
        par.assign(n, 0);
        sz.assign(n, 1);
        rng (i, 0, n) par[i] = i;
        tot = n;
    }

    int find(int x) {
        return x == par[x] ? x : par[x] = find(par[x]);
    }
    void unite(int x, int y) {
        int rx = find(x), ry = find(y);
        if(rx != ry) {
            par[rx] = ry;
            --tot;
        }
    }
};

ll fp (ll x, ll n) { //fast power: hat off to quailty
    if(n < 0) {
        x = fp(x, mod - 2);
        n = -n;
    }
    ll ans = 1;
    while(n){
        if(n&1) (ans*=x)%=mod;
        n /= 2;
        (x*=x)%=mod;
    }
    return ans;
}


vi get_popcnt(int n) {
    vi res(n + 1);
    rng (i, 0, n) {
        if (i * 2 <= n) res[i * 2] = res[i];
        if ((i & 1) == 0) res[i + 1] = res[i] + 1;
    }
    return res;
}


using idx_t = long;
template <typename  T, typename Compare = std::less<T>>
struct ST{
    size_t n; // 0-indexed
    vv<T> a;
    template <typename ptr_t>
    ST(ptr_t beg, ptr_t end):n(end-beg){
        a.resize((size_t)h_bit(n)+1); // 注意：不能写成 h_bit(n)
        a[0].assign(beg, end);
        rng (i, 0, SZ(a)-1) {
            a[i+1].resize(n);
            rng(j, 0, n - (1 << i)) {
                a[i+1][j] = min(a[i][j], a[i][j+(1<<i)], Compare());
            }
            rng(j, n-(1 << i), n) {
                a[i+1][j] = a[i][j];
            }
        }
    }

    T query(idx_t l, idx_t r) { // l <=  r
        int i = h_bit(r - l + 1);
        return min(a[i][l], a[i][r+1-(1<<i)], Compare());
    }
};





///////////////////////////////////////////////////////
const int N = 1005, M = 1005;

int main() {
    FAST_READ
#ifdef LOCAL
    ifstream in("main.in");
    cin.rdbuf(in.rdbuf());
#endif

    int n11 = 0;
    int n, m; scan(n, m);
    int occ_row = 0, occ_col = 0;

    vi col(n*m + 1), row(n*m + 1);
    vb r(n + 1, false), c(m + 1, false);

    rng (i, 1, n + 1) {
        int x;
        cin >> x;
        row[x] = i;
    }
    rng (i, 1, m + 1) {
        int x; cin >> x;
        col[x] = i;
    }

    ll ans = 1;



#define fail {println(0); return 0;}

    down (i, n * m, 1) {
        if (row[i]==0 && col[i]==0) {
            if(n11 == 0) {
                fail
            }
            ans *= n11, ans %= mod;
            --n11;
        }
        else if(row[i] == 0) {
            if (occ_row == 0 || c[col[i]]) fail;
            ans *= occ_row, ans %= mod;
            n11 += occ_row - 1;
            c[col[i]] = true;
            occ_col++;
        }
        else if(col[i] == 0) {
            if (occ_col == 0 || r[row[i]]) fail;
            ans *= occ_col; ans %= mod;
            n11 += occ_col - 1;
            r[row[i]] = true;
            occ_row++;
        }
        else {
            if(r[row[i]] || c[col[i]]) fail
            n11 += occ_row + occ_col;
            occ_row++;
            occ_col++;
            r[row[i]] = true;
            c[col[i]] = true;
        }
    }

    println(ans);







#ifdef LOCAL
    cout << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
    return 0;
}

Measured memory_bytes: 8064