using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int[] cnt = new int[N * M + 1];
		int[][] limit = new int[N][];
		bool[][] used = new bool[N][];
		for(int i=0;i<N;i++) limit[i] = new int[M];
		for(int i=0;i<N;i++) used[i] = new bool[M];
		
		for(int i=0;i<N;i++){
			for(int j=0;j<M;j++){
				limit[i][j] = Math.Min(A[i], B[j]);
				if(A[i] == B[j]){
					cnt[A[i]]++;
					if(cnt[A[i]] > 1){
						Console.WriteLine(0);
						return;
					}
					used[i][j] = true;
				}
			}
		}
		
		
		mlong ans = 1;
		int ni = N - 1;
		int mi = M - 1;
		for(int i=N*M;i>=1;i--){
			if(cnt[i] > 0){
				continue;
			}
			while(ni >= 0 && A[ni] > i) ni--;
			while(mi >= 0 && B[mi] > i) mi--;
//Console.WriteLine("{0} {1} {2}",i,ni,mi);
			if(ni >= 0 && A[ni] == i){
				int df = M - (mi + 1);
				if(df <= 0){
					Console.WriteLine(0);
					return;
				}
				ans *= df;
				continue;
			}
			if(mi >= 0 && B[mi] == i){
				int df = N - (ni + 1);
				if(df <= 0){
					Console.WriteLine(0);
					return;
				}
				ans *= df;
				continue;
			}
			{
			int df = (N - (ni + 1)) * (M - (mi + 1)) - (N * M - i);
			if(df <= 0){
				Console.WriteLine(0);
				return;
			}
			ans *= df;
			}
		}
		
		
		Console.WriteLine(ans);
	}
	int N, M;
	int[] A,B;
	const long mod = (long) 1e9 + 7;
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1];
		A = ria();
		B = ria();
		Array.Sort(A);
		Array.Sort(B);
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}


struct mlong {
	
	const long mod = (long) 1e9 + 7;
	long V;
	
	public mlong(long _v = 0){
		V = _v;
	}
	
	public static mlong operator+(mlong a, mlong b){
		var v0 = a.V + b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator-(mlong a, mlong b){
		var v0 = mod + a.V - b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator*(mlong a, mlong b){
		var v0 = a.V * b.V; if(v0 >= mod) v0 %= mod;
		return new mlong(v0);
	}
	public static mlong operator/(mlong a, mlong b){
		var v0 = a.V * inv(b.V).V; if(v0 >= mod) v0 %= mod;
		return new mlong(v0);
	}
	
	
	public static mlong inv(long x){
		long a = 0, b = 0, c = 0;
		ExtGCD(x, mod, ref a, ref b, ref c);
		return (mlong)((a + mod) % mod);
	}
	
	public static void ExtGCD(long x, long y, ref long a, ref long b, ref long c){
		long r0 = x; long r1 = y;
		long a0 = 1; long a1 = 0;
		long b0 = 0; long b1 = 1;
		long q1, r2, a2, b2;
		while(r1 > 0){
			q1 = r0 / r1;
			r2 = r0 % r1;
			a2 = a0 - q1 * a1;
			b2 = b0 - q1 * b1;
			r0 = r1; r1 = r2;
			a0 = a1; a1 = a2;
			b0 = b1; b1 = b2;
		}
		c = r0;
		a = a0;
		b = b0;
	}
	
	public static mlong ModPow(mlong a, long k){
		if(k == 0) return (mlong) 1;
		if(a == 0) return (mlong) 0;
		mlong x = a;
		mlong ret = 1;
		while(k > 0){
			if(k % 2 == 1) ret *= x;
			x *= x;
			k >>= 1;
		}
		return ret;
	}
	
	
	public static bool operator == (mlong a, mlong b){
		 return a.Equals(b);
	}
	public static bool operator != (mlong a, mlong b){
		 return !(a == b);
	}
	
	public override bool Equals(System.Object obj){
		if(obj  ==  null) return false;
		mlong p  =  (mlong) obj;
		if((System.Object) p  ==  null) return false;
		return p.V  ==  V;
	}
	public override int GetHashCode(){
		return V.GetHashCode();
	}
	
	public static implicit operator mlong(long n){
		return new mlong(n);
	}
	public static implicit operator mlong(int n){
		return new mlong(n);
	}
	public static explicit operator long(mlong n){
		return n.V;
	}
	
	public override String ToString(){
		return V.ToString();
	}
	
	
}

Measured memory_bytes: 24868