/*
URL:
https://atcoder.jp/contests/keyence2019/tasks/keyence2019_d
*/

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"sort"
	"strconv"
)

/********** FAU standard libraries **********/

//fmt.Sprintf("%b\n", 255) 	// binary expression

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()
//a := ReadFloat64()
//A := ReadFloat64Slice(n)

//str := ZeroPaddingRuneSlice(num, 32)
//str := PrintIntsLine(X...)

/*******************************************************************/

const (
	// General purpose
	MOD          = 1000000000 + 7
	ALPHABET_NUM = 26
	INF_INT64    = math.MaxInt64
	INF_BIT60    = 1 << 60
	INF_INT32    = math.MaxInt32
	INF_BIT30    = 1 << 30
	NIL          = -1

	// for dijkstra, prim, and so on
	WHITE = 0
	GRAY  = 1
	BLACK = 2
)

func init() {
	// bufio.ScanWords <---> bufio.ScanLines
	ReadString = newReadString(os.Stdin, bufio.ScanWords)
	stdout = bufio.NewWriter(os.Stdout)
}

var (
	n, m int
	A, B []int

	R, C [1000000 + 50]int
)

func main() {
	n, m = ReadInt2()
	A, B = ReadIntSlice(n), ReadIntSlice(m)

	sort.Sort(sort.Reverse(sort.IntSlice(A)))
	sort.Sort(sort.Reverse(sort.IntSlice(B)))

	comp1, _ := RunLengthEncoding(A)
	comp2, _ := RunLengthEncoding(B)
	if len(comp1) != n || len(comp2) != m {
		fmt.Println(0)
		return
	}

	for i := 1; i <= n*m; i++ {
		R[i], C[i] = -1, -1
	}
	for i := 0; i < n; i++ {
		R[A[i]] = i
	}
	for i := 0; i < m; i++ {
		C[B[i]] = i
	}

	ans := 1
	count := 0
	for i := n * m; i >= 1; i-- {
		// h, w := -1, -1
		// for j := 0; j < n; j++ {
		// 	if A[j] == i {
		// 		h = j
		// 		break
		// 	}
		// }
		// for j := 0; j < m; j++ {
		// 	if B[j] == i {
		// 		w = j
		// 		break
		// 	}
		// }
		h, w := R[i], C[i]

		if h != -1 && w != -1 {
		} else if h != -1 {
			// col := 0
			// for j := 0; j < m; j++ {
			// 	if B[j] > i {
			// 		col++
			// 	} else {
			// 		break
			// 	}
			// }

			col := BinarySearch(-1, len(B), func(mid int) bool {
				return B[mid] > i
			}) + 1

			ans *= col
		} else if w != -1 {
			// row := 0
			// for j := 0; j < n; j++ {
			// 	if A[j] > i {
			// 		row++
			// 	} else {
			// 		break
			// 	}
			// }

			row := BinarySearch(-1, len(A), func(mid int) bool {
				return A[mid] > i
			}) + 1

			ans *= row
		} else {
			// row, col := 0, 0
			// for j := 0; j < n; j++ {
			// 	if A[j] > i {
			// 		row++
			// 	} else {
			// 		break
			// 	}
			// }
			// for j := 0; j < m; j++ {
			// 	if B[j] > i {
			// 		col++
			// 	} else {
			// 		break
			// 	}
			// }

			col := BinarySearch(-1, len(B), func(mid int) bool {
				return B[mid] > i
			}) + 1
			row := BinarySearch(-1, len(A), func(mid int) bool {
				return A[mid] > i
			}) + 1

			ans *= row*col - count
		}

		ans %= MOD
		count++
	}
	fmt.Println(ans)
}

func BinarySearch(initOK, initNG int, isOK func(mid int) bool) (ok int) {
	ng := initNG
	ok = initOK
	for int(math.Abs(float64(ok-ng))) > 1 {
		mid := (ok + ng) / 2
		if isOK(mid) {
			ok = mid
		} else {
			ng = mid
		}
	}

	return ok
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// RunLengthEncoding returns encoded slice of an input.
func RunLengthEncoding(S []int) ([]int, []int) {
	runes := []int{}
	lengths := []int{}

	l := 0
	for i := 0; i < len(S); i++ {
		// 1文字目の場合保持
		if i == 0 {
			l = 1
			continue
		}

		if S[i-1] == S[i] {
			// 直前の文字と一致していればインクリメント
			l++
		} else {
			// 不一致のタイミングで追加し、長さをリセットする
			runes = append(runes, S[i-1])
			lengths = append(lengths, l)
			l = 1
		}
	}
	runes = append(runes, S[len(S)-1])
	lengths = append(lengths, l)

	return runes, lengths
}

// RunLengthDecoding decodes RLE results.
func RunLengthDecoding(S []int, L []int) []int {
	if len(S) != len(L) {
		panic("S, L are not RunLengthEncoding results")
	}

	res := []int{}

	for i := 0; i < len(S); i++ {
		for j := 0; j < L[i]; j++ {
			res = append(res, S[i])
		}
	}

	return res
}

/*******************************************************************/

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func newReadString(ior io.Reader, sf bufio.SplitFunc) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+9)) // for Codeforces
	r.Split(sf)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}
func ReadInt2() (int, int) {
	return int(readInt64()), int(readInt64())
}
func ReadInt3() (int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64())
}
func ReadInt4() (int, int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64()), int(readInt64())
}

// ReadInt64 returns as integer as int64.
func ReadInt64() int64 {
	return readInt64()
}
func ReadInt64_2() (int64, int64) {
	return readInt64(), readInt64()
}
func ReadInt64_3() (int64, int64, int64) {
	return readInt64(), readInt64(), readInt64()
}
func ReadInt64_4() (int64, int64, int64, int64) {
	return readInt64(), readInt64(), readInt64(), readInt64()
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadInt64Slice returns as int64 slice that has n integers.
func ReadInt64Slice(n int) []int64 {
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt64()
	}
	return b
}

// ReadFloat64 returns an float64.
func ReadFloat64() float64 {
	return float64(readFloat64())
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(ReadString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadFloatSlice returns an float64 slice that has n float64.
func ReadFloat64Slice(n int) []float64 {
	b := make([]float64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadFloat64()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** Debugging ***********/

// ZeroPaddingRuneSlice returns binary expressions of integer n with zero padding.
// For debugging use.
func ZeroPaddingRuneSlice(n, digitsNum int) []rune {
	sn := fmt.Sprintf("%b", n)

	residualLength := digitsNum - len(sn)
	if residualLength <= 0 {
		return []rune(sn)
	}

	zeros := make([]rune, residualLength)
	for i := 0; i < len(zeros); i++ {
		zeros[i] = '0'
	}

	res := []rune{}
	res = append(res, zeros...)
	res = append(res, []rune(sn)...)

	return res
}

// Strtoi is a wrapper of strconv.Atoi().
// If strconv.Atoi() returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// PrintIntsLine returns integers string delimited by a space.
func PrintIntsLine(A ...int) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.Itoa(A[i])
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintIntsLine returns integers string delimited by a space.
func PrintInts64Line(A ...int64) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.FormatInt(A[i], 10) // 64bit int version
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintfDebug is wrapper of fmt.Fprintf(os.Stderr, format, a...)
func PrintfDebug(format string, a ...interface{}) {
	fmt.Fprintf(os.Stderr, format, a...)
}

// PrintfBufStdout is function for output strings to buffered os.Stdout.
// You may have to call stdout.Flush() finally.
func PrintfBufStdout(format string, a ...interface{}) {
	fmt.Fprintf(stdout, format, a...)
}


Measured memory_bytes: 16384