Problem:
Score: 200 points

Problem Statement

There are three positive integers A, B and C written on a blackboard. E869120 performs the following operation K times:

Choose one integer written on the blackboard and let the chosen integer be n. Replace the chosen integer with 2n.

What is the largest possible sum of the integers written on the blackboard after K operations?

Constraints

A, B and C are integers between 1 and 50 (inclusive).

K is an integer between 1 and 10 (inclusive).

Input

Input is given from Standard Input in the following format:

A B C
K

Output

Print the largest possible sum of the integers written on the blackboard after K operations by E869220.

Sample Input 1

5 3 11
1

Sample Output 1

30

In this sample, 5, 3, 11 are initially written on the blackboard, and E869120 can perform the operation once.

There are three choices:

Double 5: The integers written on the board after the operation are 10, 3, 11.

Double 3: The integers written on the board after the operation are 5, 6, 11.

Double 11: The integers written on the board after the operation are 5, 3, 22.

If he chooses 3., the sum of the integers written on the board afterwards is 5 + 3 + 22 = 30, which is the largest among 1. through 3.

Sample Input 2

3 3 4
2

Sample Output 2

22

E869120 can perform the operation twice. The sum of the integers eventually written on the blackboard is maximized as follows:

First, double 4. The integers written on the board are now 3, 3, 8.

Next, double 8. The integers written on the board are now 3, 3, 16.

Then, the sum of the integers eventually written on the blackboard is 3 + 3 + 16 = 22.

Solution in Scala (2.11.7) (judge verdict: Accepted)

object Scanner {
  private val buf = new Array[Byte](1024); private var ptr = 0; private var len = 0
  @inline private def isPrintableChar(c: Int): Boolean = 33 <= c && c <= 126
  @inline private def hasNextByte(): Boolean =
    if (ptr >= len) { ptr = 0; len = System.in.read(buf); len > 0 } else { true }
  @inline private def hasNext(): Boolean = {
    while (hasNextByte() && !isPrintableChar(buf(ptr))) ptr += 1
    hasNextByte()
  }
  @inline private def readByte(): Byte =
    if (hasNextByte()) { val res = buf(ptr); ptr += 1; res } else { -1 }
  def next(): String = {
    if(!hasNext()) ???
    val sb = new StringBuilder; var b = readByte()
    while (isPrintableChar(b)) { sb.append(b.toChar); b = readByte() }
    sb.toString
  }
  def nextInt(): Int = {
    val n = nextLong()
    if (n < Int.MinValue || Int.MaxValue < n) ???
    n.toInt
  }
  def nextLong(): Long = {
    if(!hasNext()) ???
    var minus = false; var b = readByte()
    if (b == '-') { minus = true; b = readByte() }
    def go (b: Byte, n: Long = 0): Long =
      if ('0' <= b && b <= '9') { go(readByte(), n * 10 + b - '0') }
      else if (minus) { -n } else { n }
    go(b)
  }
  def nextDouble(): Double = next.toDouble
}

object Main extends App{
  val a,b,c,k = Scanner.nextInt()
  val array = Array(a,b,c).sorted
  val doubled = array.last * scala.math.pow(2,k).toInt
  println(doubled+array.init.sum)
}