Problem:
Score : 200 points

Problem Statement

We have a board with H horizontal rows and W vertical columns of squares.
There is a bishop at the top-left square on this board.
How many squares can this bishop reach by zero or more movements?

Here the bishop can only move diagonally.
More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:

r_1 + c_1 = r_2 + c_2

r_1 - c_1 = r_2 - c_2

For example, in the following figure, the bishop can move to any of the red squares in one move:

Constraints

1 \leq H, W \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H \ W

Output

Print the number of squares the bishop can reach.

Sample Input 1

4 5

Sample Output 1

10

The bishop can reach the cyan squares in the following figure:

Sample Input 2

7 3

Sample Output 2

11

The bishop can reach the cyan squares in the following figure:

Sample Input 3

1000000000 1000000000

Sample Output 3

500000000000000000

Solution in Scala (2.11.7) (judge verdict: Wrong Answer)

//import java.util.Scanner

import java.io._
import java.nio.file.Files._
import java.nio.file.Path
import java.util.StringTokenizer

import scala.collection.immutable._
import scala.io.Codec

/**
  * Scala implementation of a faster java.util.Scanner
  * See: http://codeforces.com/blog/entry/7018
  */

class Scanner(reader: LineNumberReader) extends Iterable[String] with AutoCloseable {
  def this(reader: BufferedReader) = this(new LineNumberReader(reader))

  def this(reader: Reader) = this(new BufferedReader(reader))

  def this(inputStream: InputStream)(implicit codec: Codec) = this(new InputStreamReader(inputStream, codec.charSet))

  def this(path: Path)(implicit codec: Codec) = this(newBufferedReader(path, codec.charSet))

  def this(file: File)(implicit codec: Codec) = this(file.toPath)(codec)

  def this(str: String) = this(new StringReader(str))

  override def iterator: Iterator[String] = for {
    line <- Iterator.continually(reader.readLine()).takeWhile(_ != null)
    tokenizer = new StringTokenizer(line)
    tokens <- Iterator.continually(tokenizer).takeWhile(_.hasMoreTokens)
  } yield tokens.nextToken()

  private[this] var current = iterator

  def hasNext: Boolean = current.hasNext

  @inline def next(): String = current.next()

  /**
    * This is different from Java's scanner.nextLine
    * The Java one is a misnomer since it actually travel to end of current line
    * This one actually does fetch the next line
    */
  def nextLine(): String = {
    val line = reader.readLine()
    current = iterator
    line
  }

  def lineNumber: Int = reader.getLineNumber

  def nextString(): String = next()

  def nextBoolean(): Boolean = next().toBoolean

  def nextByte(radix: Int = 10): Byte = java.lang.Byte.parseByte(next(), radix)

  def nextShort(radix: Int = 10): Short = java.lang.Short.parseShort(next(), radix)

  def nextInt(radix: Int = 10): Int = java.lang.Integer.parseInt(next(), radix)

  def nextLong(radix: Int = 10): Long = java.lang.Long.parseLong(next(), radix)

  def nextBigInt(radix: Int = 10): BigInt = BigInt(next(), radix)

  def nextFloat(): Float = next().toFloat

  def nextDouble(): Double = next().toDouble

  def nextBigDecimal(): BigDecimal = BigDecimal(next())

  override def close(): Unit = reader.close()
}


class IUnionFind(val size: Int) {

  private case class Node(var parent: Option[Int], var treeSize: Int)

  private val nodes = Array.fill[Node](size)(Node(None, treeSize = 1))

  def union(t1: Int, t2: Int): IUnionFind = {
    if (t1 == t2) return this

    val root1 = root(t1)
    val root2 = root(t2)
    if (root1 == root2) return this

    val node1 = nodes(root1)
    val node2 = nodes(root2)

    if (node1.treeSize < node2.treeSize) {
      node1.parent = Some(t2)
      node2.treeSize += node1.treeSize
    } else {
      node2.parent = Some(t1)
      node1.treeSize += node2.treeSize
    }
    this
  }

  def connected(t1: Int, t2: Int): Boolean = t1 == t2 || root(t1) == root(t2)

  def root(t: Int): Int = nodes(t).parent match {
    case None => t
    case Some(p) =>
      nodes(t).parent = Some(root(p))
      nodes(t).parent.get
  }
}


object Main {
  def solve(sc: => Scanner): Unit = {
    val A, B = sc.nextLong()
    println(A * (B / 2) + (A + 1) / 2 * (B % 2))
  }

  def flip(A: Array[Boolean], B: Array[(Int, Long)]): Array[(Int, Long)] = {
    B.map { case (index, _) =>
      (index, (if (0 < index && A(index - 1)) B(index - 1)._2 else 0L) + (if (index + 1 < B.length && !A(index + 1)) B(index + 1)._2 else 0L))
    }
  }

  val mod: Long = (1e9 + 7).toLong

  def recursive(N: Int, canUse: Int = 0, nowString: String = ""): Array[String] = {
    if (N == 0) Array(nowString)
    else (0 to canUse).flatMap(i => recursive(N - 1, math.max(canUse, i + 1), nowString + (i + 'a').toChar)).toArray
  }

  @scala.annotation.tailrec
  def factorial(now: Long, ans: Long = 1): Long = {
    if (now == 0) 0 else if (now == 1) ans else factorial(now - 1, now * ans)
  }

  implicit class implicitInt(val N: Int) {
    def times[B](function: Int => B): IndexedSeq[B] = (0 until N).map(function)
  }

  def calc(input: (Long, Long, Long, Long, Long, Long)): Long = {
    input match {
      case (a, b, c, x, y, z) => {
        var ans: Long = Long.MaxValue
        if (b >= 3 && (a >= 2 || c >= 2)) {
          ans = Math.min(ans, Math.max(a - (b - 1), 0) * x + Math.max(c - Math.min(a - 1, b - 2), 0) * z)
          ans = Math.min(ans, Math.max(a - Math.min(c - 1, b - 2), 0) * x + Math.max(c - (b - 1), 0) * z)
        }
        //        println(ans)
        if (b >= 2 && (a >= b && c >= b + 1)) {
          ans = Math.min(ans, y + Math.max(0, a - (c - 1)) * x)
        }
        //        println(ans)
        if (b >= 2 && (a >= b + 1 && c >= b)) {
          ans = Math.min(ans, y + Math.max(0, c - (a - 1)) * z)
        }
        //        println(ans)
        if (a >= 2 && c >= 2)
          if (a != c)
            ans = Math.min(ans, Math.max(0, b - (Math.min(a, c) - 1)) * y)
          else if (a >= 3 && c >= 3)
            ans = Math.min(ans, Math.max(0, b - (Math.min(a, c) - 2)) * y + Math.min(x, z))
        //        println(ans)
        if (ans == Long.MaxValue) ans = -1
        ans
      }
    }
  }

  def time(s: String): Int =
    s.substring(0, 2).toInt * 60 + s.substring(3, 5).toInt

  def getPermutation(begin: Long = 0): Stream[Long] =
    Stream.cons(begin, getPermutation(begin + 1))

  def getFibonacci(prevprev: Long = 0, prev: Long = 1): Stream[Long] =
    Stream.cons(prevprev, getFibonacci(prev, prevprev + prev))

  @scala.annotation.tailrec
  def recursive2(X: Set[Long], Y: Stream[Long]): Long = if (X.contains(Y.head)) X.size else recursive2(X + Y.head, Y.tail)

  def check(i: Int, X: String): Long = {
    if (X == "") 0 else check(i, X.tail) * i + X.head.toString.toLong
  }

  def shift(n: Long): Long = {
    if (n == 0) 0
    else if (n == 1) 1
    else shift(n - 1) << 1
  }

  def unShift(n: Long): Long = {
    if (n == 0) 0
    else unShift(n >> 1) + 1
  }

  @scala.annotation.tailrec
  def gcd(i: Long, j: Long): Long = {
    if (i < j) gcd(j, i)
    else if (j == 0) i
    else gcd(j, i % j)
  }

  def primeFactors(i: Long): List[Long] = primeFactors_(i, 1).sorted


  def primeFactors_(i: Long, j: Long): List[Long] = {
    if (j * j > i) List.empty else if (i % j == 0) primeFactors_(i, j + 1) ++ List[Long](j, i / j) else primeFactors_(i, j + 1)
  }

  def main(args: Array[String]): Unit = {
    val sc: Scanner = new Scanner(System.in)
    solve(sc)
  }
}

object Util {
  def getPermutation(begin: Long = 0): Stream[Long] =
    Stream.cons(begin, getPermutation(begin + 1))

  def getPrimeList: Stream[Long] =
    getPrimeListRecursive(getPermutation(begin = 2))

  private def getPrimeListRecursive(A: Stream[Long]): Stream[Long] =
    Stream.cons(A.head, getPrimeListRecursive(A.tail.filter(_ % A.head != 0)))

  def fib(a: Long = 0, b: Long = 1, mod: Long = Long.MaxValue): Stream[Long] = a #:: fib(b % mod, (a + b) % mod, mod)
}

object ArabicRoman {

  type =?>[A, B] = PartialFunction[A, B]

  private val codeTable: List[(Int, String)] = List(
    (1000, "M"), (900, "CM"), (500, "D"), (400, "CD"), (100, "C"),
    (90, "XC"), (50, "L"), (40, "XL"), (10, "X"), (9, "IX"), (5, "V"), (4, "IV"), (1, "I"))

  val arabicToRoman: Int =?> String = {
    case src if src >= 1 && src <= 3999 =>

      @scala.annotation.tailrec
      def convert(left: Int, cont: String = "", code: List[(Int, String)] = codeTable): String = {
        val (unitVal, unitChar) = code.head
        left - unitVal match {
          case n if n == 0 => cont + unitChar
          case n if n > 0 => convert(n, cont + unitChar, code)
          case _ => convert(left, cont, code.tail)
        }
      }

      convert(src)
  }

  val romanToArabic: String =?> Int = {
    case src if Option(src).exists { s => {
      s.nonEmpty && """[^MDCLXVI]""".r.findFirstMatchIn(s.toUpperCase).isEmpty
    }
    } =>

      @scala.annotation.tailrec
      def convert(left: String, cont: Int = 0, code: List[(Int, String)] = codeTable): Int = {
        val (unitVal, unitChar) = code.head
        left.splitAt(unitChar.length) match {
          case ("", _) => cont
          case (`unitChar`, tail) => convert(tail, cont + unitVal, code)
          case _ => convert(left, cont, code.tail)
        }
      }

      convert(src.toUpperCase())
  }
}

object PowMod {
  def naivePowMod(a: Long, k: Long, m: Long): Long = {
    var t: Long = 1
    val aMod: Long = a % m

    for (_ <- 1L to k) {
      t = ((t % m) * aMod) % m
    }
    t.toInt
  }

  def powMod(a: Long, k: Long, m: Long): Long = {
    if (k == 0) 1
    else {
      val t = powMod(a, k / 2, m)
      if ((k % 2) == 0) (t * t) % m else (((t * t) % m) * a) % m
    }
  }
}