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Contest: Task: Related: TaskA TaskC

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:

  1. Double $5$: The integers written on the board after the operation are $10, 3, 11$.
  2. Double $3$: The integers written on the board after the operation are $5, 6, 11$.
  3. 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 $3 + 3 + 16 = 22$.