#include <bits/stdc++.h>

using namespace std;

#define countof(a) (sizeof(a)/sizeof(*a))

#define vi vector<int>
#define vvi vector<vector<int> >
#define vpi vector<pi >
#define pi pair<int,int>
#define mp make_pair
#define fi first
#define se second
#define all(n) n.begin(), n.end()

#define FROMTO(var, from, to) for (register int var = (from), var##down = ((int)(to)) < ((int)(from));var##down ? (var >= (int)(to)) : (var <= (int)(to));var##down ? var-- : var++)
#define UPTO(var, from, to)   for (register int var = (from); var <= ((int)to); var++)
#define DOWNTO(var, from, to) for (register int var = (from); var >= ((int)to); var--)
#define FOR(var, to)          UPTO(var, 0, (to)-1)
#define DOWN(var, from)       DOWNTO(var, (from)-1, 0) 

#define INIT(var, val) FOR(i,countof(var)) var[i] = val
#define INPUT(var) FOR(i,countof(var)) cin >> var[i]
#define INPUT1(var) FOR(i,countof(var)) cin >> var[i], var[i]--

#define SORT(v) qsort(v,countof(v),sizeof(*v),int_less)
#define SORTT(v) qsort(v,countof(v),sizeof(*v),int_greater)
#define QSORT(v,b) qsort(v,countof(v),sizeof(*v),b)

#define MOD 1000000007
#define INF ((1 << 30)-1)
#define LINF ((1LL << 62)-1)

typedef uint8_t u8;
typedef uint16_t u16;
typedef uint32_t u32;
typedef uint64_t u64;
typedef int8_t s8;
typedef int16_t s16;
typedef int32_t s32;
typedef int64_t s64;

struct Comb {
    vector<vector<s64> > data;
    Comb(int n) { // O(n^2)
        data = vector<vector<s64> >(n+1,vector<s64>(n+1,1));
        UPTO(i,1,n) {
            FOR(j,i+1) {
                if (!j || j == i) data[i][j] = 1;
                else data[i][j] = data[i-1][j-1] + data[i-1][j];
            }
        }
    }
    
    s64 ncr(int n, int r) {
        return data[n][r];
    }
};

static inline int ri() {
  int a;
  scanf("%d", &a);
  return a;
}


template<int mod>
struct ModInt{
    int x;
    ModInt():x(0){}
    ModInt(long long 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;}
    explicit operator int() const { return x; }                           // added by QCFium
    ModInt operator=(const int p) {x = p; return ModInt(*this);} // added by QCFium
    ModInt inverse()const{
        int a=x,b=mod,u=1,v=0,t;
        while(b>0){
            t=a/b;
            a-=t*b;
            swap(a,b);
            u-=t*v;
            swap(u,v);
        }
        return ModInt(u);
    }
    friend ostream &operator<<(ostream &os,const ModInt<mod> &p){
        return os<<p.x;
    }
    friend istream &operator>>(istream &is,ModInt<mod> &a){
        long long x;
        is>>x;
        a=ModInt<mod>(x);
        return (is);
    }
};
typedef ModInt<MOD> mint;

mint mpow(s64 num, s64 times) { // O(log(times))
    mint next = num%MOD;
	mint res = 1;
	while (times) {
		if (times%2)
            res *= next;
		next *= next;
		times /= 2;
	}
	return res;
}

struct MComb {
    vector<mint> fact;
    vector<mint> inversed;
    MComb(int n) { // O(n+log(mod))
        fact = vector<mint>(n+1,1);
        UPTO(i,1,n) fact[i] = fact[i-1]*mint(i);
        inversed = vector<mint>(n+1);
        inversed[n] = mpow((int)fact[n], MOD-2);
        DOWN(i,n) inversed[i]=inversed[i+1]*mint(i+1);
    }
    
    mint ncr(int n, int r) {
        return (fact[n] * inversed[r] * inversed[n-r]);
    }
    
    mint npr(int n, int r) {
        return (fact[n] * inversed[n-r]);
    }
    
    mint nhr(int n, int r) {
        assert(n+r-1 < (int)fact.size());
        return ncr(n+r-1, r);
    }
};


int int_less(const void *a, const void *b) {
  return (*((const int*)a) - *((const int*)b));
}
int int_greater(const void *a, const void *b) {
  return (*((const int*)b) - *((const int*)a));
}



int main() {
	int n = ri(), m = ri();
	vi a(n); FOR(i,n) a[i] = ri(); sort(all(a));
	vi b(m); FOR(i,m) b[i] = ri(); sort(all(b));
	FOR(i,n-1) if (a[i] == a[i+1]) { cout << 0 << endl; return 0; }
	FOR(i,m-1) if (b[i] == b[i+1]) { cout << 0 << endl; return 0; }
	if (a[n-1] != n*m || b[m-1] != n*m) { cout << 0 << endl; return 0; }
	MComb com(n*m+1);
	set<int> al;
	FOR(i,n) al.insert(a[i]);
	FOR(i,m) al.insert(b[i]);
	vector<pair<int,int> > ranges;
	int last = 0;
	for (auto i : al) {
		if (i && last+1 <= i-1) {
			ranges.push_back({last+1, i-1});
		}
		ranges.push_back({i,i});
		last = i;
	}
	int used = 0;
	mint res = 1;
	DOWN(j,ranges.size()) {
		auto i = ranges[j];
		if (i.fi != i.se || !al.count(i.fi)) { // interval
			// i.se+1以上
			auto x = lower_bound(all(a),i.se+1);
			auto y = lower_bound(all(b),i.se+1);
			if (x == a.end() || y == b.end()) {
				cout << 0 << endl;
				return 0;
			}
			int xx = a.end()-x;
			int yy = b.end()-y;
			int num = i.se-i.fi+1;
			if (xx*yy < num+used) {
				cout << 0 << endl;
				return 0;
			}
			res *= com.npr(xx*yy-used, num);
			used += num;
			////////////////////////////////
		} else {
			auto x = lower_bound(all(a),i.fi);
			auto y = lower_bound(all(b),i.fi);
			if (x == a.end() || y == b.end()) {
				cout << 0 << endl;
				return 0;
			}
			int xx = a.end()-x;
			int yy = b.end()-y;
			if (*x == i.fi && *y == i.se) {
				if (xx*yy <= used) {
					cout << 0 << endl;
					return 0;
				}
				used++;
			} else {
				if (*x == i.fi) {
					res *= yy;
				} else res *= xx;
				used++;
			}
		}
	}
	cout << res << endl;
    return 0;
}


Measured memory_bytes: 8192