#include<cassert>
#include<stdio.h>
#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<string.h>
using namespace std;

typedef long long LL;
typedef vector<int> VI;

#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define EACH(i,c) for(__typeof((c).begin()) i=(c).begin(),i##_end=(c).end();i!=i##_end;++i)
#define eprintf(...) fprintf(stderr, __VA_ARGS__)

template<class T> inline void amin(T &x, const T &y) { if (y<x) x=y; }
template<class T> inline void amax(T &x, const T &y) { if (x<y) x=y; }
template<class Iter> void rprintf(const char *fmt, Iter begin, Iter end) {
    for (bool sp=0; begin!=end; ++begin) { if (sp) putchar(' '); else sp = true; printf(fmt, *begin); }
    putchar('\n');
}
template<unsigned MOD> struct ModInt {
    static const unsigned static_MOD = MOD;
    unsigned x;
    void undef() { x = (unsigned)-1; }
    bool isnan() const { return x == (unsigned)-1; }
    inline int geti() const { return (int)x; }
    ModInt() { x = 0; }
    ModInt(const ModInt &y) { x = y.x; }
    ModInt(int y) { if (y<0 || (int)MOD<=y) y %= (int)MOD; if (y<0) y += MOD; x=y; }
    ModInt(unsigned y) { if (MOD<=y) x = y % MOD; else x = y; }
    ModInt(long long y) { if (y<0 || MOD<=y) y %= MOD; if (y<0) y += MOD; x=y; }
    ModInt(unsigned long long y) { if (MOD<=y) x = y % MOD; else x = y; }
    ModInt &operator+=(const ModInt y) { if ((x += y.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator-=(const ModInt y) { if ((x -= y.x) & (1u<<31)) x += MOD; return *this; }
    ModInt &operator*=(const ModInt y) { x = (unsigned long long)x * y.x % MOD; return *this; }
    ModInt &operator/=(const ModInt y) { x = (unsigned long long)x * y.inv().x % MOD; return *this; }
    ModInt operator-() const { return (x ? MOD-x: 0); }

    ModInt inv() const {
	unsigned a = MOD, b = x; int u = 0, v = 1;
	while (b) {
	    int t = a / b;
	    a -= t * b; swap(a, b);
	    u -= t * v; swap(u, v);
	}
	if (u < 0) u += MOD;
	return ModInt(u);
    }
    ModInt pow(long long y) const {
	ModInt b = *this, r = 1;
	if (y < 0) { b = b.inv(); y = -y; }
	for (; y; y>>=1) {
	    if (y&1) r *= b;
	    b *= b;
	}
	return r;
    }
    friend ModInt operator+(ModInt x, const ModInt y) { return x += y; }
    friend ModInt operator-(ModInt x, const ModInt y) { return x -= y; }
    friend ModInt operator*(ModInt x, const ModInt y) { return x *= y; }
    friend ModInt operator/(ModInt x, const ModInt y) { return x *= y.inv(); }
    friend bool operator<(const ModInt x, const ModInt y) { return x.x < y.x; }
    friend bool operator==(const ModInt x, const ModInt y) { return x.x == y.x; }
    friend bool operator!=(const ModInt x, const ModInt y) { return x.x != y.x; }
};

const LL MOD = 1000000007;
typedef ModInt<MOD> Mint;

int N, M;
int A[1111];
int B[1111];
int row[1000111];
int col[1000111];
int A_pool[1111];
int B_pool[1111];
int use[1111][1111];


void MAIN() {
    scanf("%d%d", &N, &M);
    REP (i, N) scanf("%d", A+i);
    REP (i, M) scanf("%d", B+i);

//#ifdef LOCAL
//    N = 1000;
//    M = 1000;
//    REP (i, N) A[i] = B[i] = 1000000 - 999 + i;
//#endif


    bool yes = true;
    memset(row, -1, sizeof row);
    memset(col, -1, sizeof col);
    REP (i, N) {
	if (row[A[i]] >= 0) yes = false;
	row[A[i]] = i;
    }
    REP (j, M) {
	if (col[B[j]] >= 0) yes = false;
	col[B[j]] = j;
    }
    if (row[N*M] == -1 || col[N*M] == -1) yes = false;

    if (yes) {
	Mint ans = 1;
	int rest = 0;

	for (int cur=N*M; cur>=1; cur--) {
	    int r = row[cur], c = col[cur];
	    if (r >= 0 && c >= 0) {
		assert(use[r][c] == 0);
		use[r][c] = 2;
		REP (i, N) {
		    if (use[i][c] == 1) rest++;
		    use[i][c]++;
		    A_pool[i]++;
		}
		REP (j, M) {
		    if (use[r][j] == 1) rest++;
		    use[r][j]++;
		    B_pool[j]++;
		}
	    } else if (r >= 0) {
		ans *= A_pool[r];
		REP (j, M) {
		    if (use[r][j] == 1) rest++;
		    else B_pool[j]++;
		    use[r][j]++;
		}
		rest--;
	    } else if (c >= 0) {
		ans *= B_pool[c];
		REP (i, N) {
		    if (use[i][c] == 1) rest++;
		    else A_pool[i]++;
		    use[i][c]++;
		}
		rest--;
	    } else {
		ans *= rest;
		rest--;
	    }
	    if (rest < 0) ans = 0;
	}

	printf("%d\n", ans.geti());
    } else {
	puts("0");
    }
}

int main() {
    int TC = 1;
//    scanf("%d", &TC);
    REP (tc, TC) MAIN();
    return 0;
}



Measured memory_bytes: 12928