object Main {
  def main(args: Array[String]): Unit = {
    val s = new Main()
    s.solve()
    s.out.flush()
  }
}

class Main {
  import java.io._
  import java.util.StringTokenizer

  import scala.collection.mutable
  import scala.util.Sorting
  import math.{abs, max, min}
  import mutable.{ArrayBuffer, ListBuffer}
  import scala.reflect.ClassTag

  val MOD = 1000000007
  val out = new PrintWriter(System.out)

  /**
    * @param tpe 0: row, 1: col, 2, どっちも
    */
  case class Restriction(tpe: Int, v: Int)

  def solve(): Unit = {
    val N, M = ni()
    val A = na(N)
    val B = na(M)

    val inRow = A.toSet
    val inCol = B.toSet
    val restrictions = ArrayBuffer[Restriction]()

    REP(N) { i =>
      val tpe = if (inCol.contains(A(i))) 2 else 0
      restrictions += Restriction(tpe, A(i))
    }

    REP(M) { i =>
      if (!inRow.contains(B(i))) restrictions += Restriction(1, B(i))
    }

    // vの降順でそーとしてある
    var ans = 1L
    var cur = N * M + 1
    val R = restrictions.sortBy(_.v).reverse

    def calc(): Long = {
      var r, c = 0

      // cur+1からuntil手前までシミュレートする
      def place(until: Int): Boolean = {
        var i = cur - 1
        while (i > until) {
          val alreadyPlaced = N * M - i
          val free = r * c - alreadyPlaced
          if (free <= 0) return false
          ans = ans * free % MOD
          i -= 1
        }

        true
      }

      REP(R.length) { i =>
        R(i).tpe match {
          // row
          case 0 =>
            if (!place(R(i).v)) return 0
            ans = (ans * c) % MOD
            cur = R(i).v
            r += 1

          // col
          case 1 =>
            if (!place(R(i).v)) return 0
            ans = (ans * r) % MOD
            cur = R(i).v
            c += 1

          // どっちも
          case 2 =>
            if (!place(R(i).v)) return 0
            cur = R(i).v
            c += 1
            r += 1
        }
      }

      place(0)

      ans
    }

    def validate(X: Array[Int]) = {
      X.max == N * M && X.groupBy(identity).values.forall(_.length == 1)
    }

    if (validate(A) && validate(B)) {
      out.println(calc())
    } else {
      out.println(0)
    }
  }
  

  def debug(as: Array[Boolean]): Unit = {
    System.err.println(as.map(x => if(x) "1" else "0").mkString)
  }

  def debug(as: Array[Int]): Unit = {
    System.err.println(as.mkString(" "))
  }

  def debug(as: Array[Long]): Unit = {
    System.err.println(as.mkString(" "))
  }

  def debug(s: String): Unit = {
    System.err.println(s)
  }

  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next().toInt
    def nextLong(): Long = next().toLong
    def nextChar(): Char = next().charAt(0)
  }
  val sc = new InputReader(System.in)
  def ni(): Int = sc.nextInt()
  def nl(): Long = sc.nextLong()
  def nc(): Char = sc.nextChar()
  def ns(): String = sc.next()
  def ns(n: Int): Array[Char] = ns().toCharArray
  def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)
  def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
    val A1, A2 = Array.ofDim[Int](n)
    REP(n) { i =>
      A1(i) = ni() + offset
      A2(i) = ni() + offset
    }
    (A1, A2)
  }
  def nm(n: Int, m: Int): Array[Array[Int]] = {
    val A = Array.ofDim[Int](n, m)
    REP(n) { i =>
      REP(m) { j =>
        A(i)(j) = ni()
      }
    }
    A
  }
  def nal(n: Int): Array[Long] = map(n)(_ => nl())
  def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }

  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }


  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }

  def cumSum(as: Array[Int]) = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}

Measured memory_bytes: 30760