using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class KEYENCE2019D
    {
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var M = NN;
            var AList = NNList(N);
            var BList = NNList(M);
            if (AList.Distinct().Count() != AList.Count() || BList.Distinct().Count() != BList.Count())
            {
                Console.WriteLine(0);
                return;
            }
            var sortedA = AList.OrderByDescending(e => e).ToList();
            var sortedB = BList.OrderByDescending(e => e).ToList();
            sortedA.Add(0);
            sortedB.Add(0);
            LIB_Mod ans = 1;
            var aIdx = 0;
            var bIdx = 0;
            for (var i = N * M; i > 0; i--)
            {
                while (sortedA[aIdx] > i) ++aIdx;
                while (sortedB[bIdx] > i) ++bIdx;
                if (sortedA[aIdx] == i && sortedB[bIdx] == i) ans *= 1;
                else if (sortedA[aIdx] != i && sortedB[bIdx] == i) ans *= aIdx;
                else if (sortedA[aIdx] == i && sortedB[bIdx] != i) ans *= bIdx;
                else
                {
                    LIB_Mod tmp = aIdx;
                    tmp *= bIdx;
                    ans *= tmp - (N * M - i);
                }
            }
            Console.WriteLine(ans);
        }
        static class Console_
        {
            static Queue<string> param = new Queue<string>();
            public static string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static public void Main(string[] args) { if (args.Length == 0) { Console.SetOut(new Printer(Console.OpenStandardOutput())); } var t = new Thread(Solve, 134217728); t.Start(); t.Join(); Console.Out.Flush(); }
        static long NN => long.Parse(Console_.NextString());
        static double ND => double.Parse(Console_.NextString());
        static string NS => Console_.NextString();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static IEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => x.OrderBy(_ => xorshift);
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    struct LIB_Mod : IEquatable<LIB_Mod>, IEquatable<long>
    {
        static public long _mod = 1000000007; long v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_Mod(long x)
        {
            if (x < _mod && x >= 0) v = x;
            else if ((v = x % _mod) < 0) v += _mod;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public implicit operator LIB_Mod(long x) => new LIB_Mod(x);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public implicit operator long(LIB_Mod x) => x.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Add(LIB_Mod x) { if ((v += x.v) >= _mod) v -= _mod; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Sub(LIB_Mod x) { if ((v -= x.v) < 0) v += _mod; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Mul(LIB_Mod x) => v = (v * x.v) % _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Div(LIB_Mod x) => v = (v * Inverse(x.v)) % _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator +(LIB_Mod x, LIB_Mod y) { var t = x.v + y.v; return t >= _mod ? new LIB_Mod { v = t - _mod } : new LIB_Mod { v = t }; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator -(LIB_Mod x, LIB_Mod y) { var t = x.v - y.v; return t < 0 ? new LIB_Mod { v = t + _mod } : new LIB_Mod { v = t }; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator *(LIB_Mod x, LIB_Mod y) => x.v * y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator /(LIB_Mod x, LIB_Mod y) => x.v * Inverse(y.v);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public bool operator ==(LIB_Mod x, LIB_Mod y) => x.v == y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public bool operator !=(LIB_Mod x, LIB_Mod y) => x.v != y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long Inverse(long x)
        {
            long b = _mod, r = 1, u = 0, t = 0;
            while (b > 0)
            {
                var q = x / b;
                t = u;
                u = r - q * u;
                r = t;
                t = b;
                b = x - q * b;
                x = t;
            }
            return r < 0 ? r + _mod : r;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(LIB_Mod x) => v == x.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(long x) => v == x;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override bool Equals(object x) => x == null ? false : Equals((LIB_Mod)x);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override int GetHashCode() => v.GetHashCode();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string ToString() => v.ToString();
        static List<LIB_Mod> _fact = new List<LIB_Mod>() { 1 };
        static long _factm = _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void B(long n)
        {
            if (_factm != _mod) _fact = new List<LIB_Mod>() { 1 };
            if (n >= _fact.Count)
                for (int i = _fact.Count; i <= n; ++i)
                    _fact.Add(_fact[i - 1] * i);
            _factm = _mod;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Comb(long n, long k)
        {
            B(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Perm(long n, long k)
        {
            B(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Pow(LIB_Mod x, long y)
        {
            LIB_Mod a = 1;
            while (y != 0)
            {
                if ((y & 1) == 1) a.Mul(x);
                x.Mul(x);
                y >>= 1;
            }
            return a;
        }
    }
}


Measured memory_bytes: 15572