100961: [AtCoder]ABC096 B - Maximum Sum
Description
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 $3 + 3 + 16 = 22$.