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///YEAH IM THE BEST I'VE EVER WAS

///SO HAPPY

#include <bits/stdc++.h>

#define popcnt(x) __builtin_popcount(x)

#define fr first

#define sc second

#define m_p make_pair

#define low_bo(a, x) lower_bound(a.begin(), a.end(), x) - a.begin()

#define up_bo(a, x) upper_bound(a.begin(), a.end(), x) - a.begin()

#define unique(a) a.resize(unique(a.begin(), a.end()) - a.begin())

#define popcnt(x) __builtin_popcount(x)

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

//using namespace __gnu_pbds;

//gp_hash_table<int, int> table;

//#pragma GCC optimize("O3")
//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
//#pragma GCC target("avx,tune=native")
//float __attribute__((aligned(32)))

/*char memory[(int)1e8];

char memorypos;

inline void * operator new(size_t n){
    char * ret = memory + memorypos;
    memorypos += n;
    return (void *)ret;
}

inline void operator delete(void *){}
*/

using namespace std;

typedef long long ll;

typedef unsigned long long ull;

typedef long double ld;

typedef unsigned int uint;

ll sqr(ll x){
    return x * x;
}

int mysqrt(ll x){
    int l = 0, r = 1e9 + 1;
    while (r - l > 1){
        int m = (l + r) / 2;
        if (m * (ll)m <= x)
            l = m;
        else
            r = m;
    }
    return l;
}

#ifdef ONPC
    mt19937 rnd(231);
    mt19937_64 rndll(231);
#else
    mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
    mt19937_64 rndll(chrono::high_resolution_clock::now().time_since_epoch().count());
#endif
ll AR = 19, BR = 13, CR = 23, XR = 228, YR = 322, MODR = 1e9 + 993;

ll myrand(){
    ll ZR = (XR * AR + YR * BR + CR) % MODR;
    XR = YR;
    YR = ZR;
    return ZR;
}

int gcd(int a, int b){
    return a ? gcd(b % a, a) : b;
}

int gcdex(int a, int b, int &x, int &y){
    if (a == 0){
        x = 0;
        y = 1;
        return b;
    }
    int x1, y1;
    int ret = gcdex(b % a, a, x1, y1);
    x = y1 - (b / a) * x1;
    y = x1;
    return ret;
}

const int Mod = 1e9 + 7;

int Bpow(int x, ll y){
    int ret = 1;
    int w = x;
    while (y){
        if (y & 1)
            ret = (ret * (ll)w) % Mod;
        w = (w * (ll)w) % Mod;
        y >>= 1;
    }
    return ret;
}

int Bdiv(int x){
    int a, b;
    gcdex(x, Mod, a, b);
    if (a < 0)
        a += Mod;
    return a;
}

int Bdiv(int x, int y){
    return (x * (ll)Bpow(y, Mod - 2)) % Mod;
}

inline int ad(int x, int y){
    return x + y >= Mod ? x + y - Mod : x + y;
}

inline int dif(int x, int y){
    return x - y < 0 ? x - y + Mod : x - y;
}

inline int mul(int x, int y){
    return (x * (ll)y) % Mod;
}

int inv(int a){
    int b = Mod, x = 0, y = 1;
    while (a){
        int t = b / a;
        b -= a * t;
        x -= t * y;
        swap(a, b);
        swap(x, y);
    }
    if (x < 0)
        x += Mod;
    return x;
}

void setmin(int &x, int y){
    x = min(x, y);
}

void setmax(int &x, int y){
    x = max(x, y);
}

void setmin(ll &x, ll y){
    x = min(x, y);
}

void setmax(ll &x, ll y){
    x = max(x, y);
}

const ll llinf = 1e18 + 100;

const ld eps = 1e-9;

const int maxn = 2e5 + 100, maxw = 1e6 + 100, inf = 2e9 + 100, sq = 600, X = 43, LG = 17;



int main()
{
    #ifdef ONPC
    //ifstream cin("a.in");
    //ofstream cout("a.out");
    freopen("a.in", "r", stdin);
    freopen("a.out", "w", stdout);
    #else
    //ifstream cin("gymnasts.in");
    //ofstream cout("gymnasts.out");
    //freopen("nextpartition.in", "r", stdin);
    //freopen("nextpartition.out", "w", stdout);
    #endif // ONPC
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int n, m;
    cin >> n >> m;
    vector<int> a(n * m, -1), b(n * m, -1), A(n), B(m);
    for (int i = 0; i < n; i++) {
        int w;
        cin >> w;
        w--;
        A[i] = w;
        if (a[w] != -1) {
            cout << 0;
            return 0;
        }
        a[w] = i;
    }
    for (int i = 0; i < m; i++) {
        int w;
        cin >> w;
        w--;
        B[i] = w;
        if (b[w] != -1) {
            cout << 0;
            return 0;
        }
        b[w] = i;
    }
    int ans = 1;
    int x = 0, y = 0;
    for (int i = n * m - 1; i >= 0; i--) {
        if (a[i] + b[i] == -2) {
            int o = x * y - (n * m - i - 1);
            if (o <= 0) {
                cout << 0;
                return 0;
            }
            ans = mul(ans, o);
            continue;
        }
        if (a[i] != -1 && b[i] != -1) {
            x++;
            y++;
            continue;
        }
        if (a[i] != -1) {
            int o = 0;
            for (int it = 0; it < m; it++)
            if (B[it] > i) {
                o++;
            }
            if (o == 0) {
                cout << 0;
                return 0;
            }
            x++;
            ans = mul(ans, o);
            continue;
        }
        if (b[i] != -1) {
            int o = 0;
            for (int it = 0; it < n; it++)
            if (A[it] > i) {
                o++;
            }
            if (o == 0) {
                cout << 0;
                return 0;
            }
            y++;
            ans = mul(ans, o);
            continue;
        }
    }
    cout << ans;
}


Measured memory_bytes: 8064