Maximum Sum

AtCoder

IDabc096_b

Time2000ms

Memory256MB

Difficulty—

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: $A$ $B$ $C$ $K$ [samples]

Samples

Input #1

5 3 11
1

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.

Input #2

3 3 4
2

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 $3 + 3 + 16 = 22$.

API Response (JSON)

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  "problem": {
    "name": "Maximum Sum",
    "description": {
      "content": "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 int",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc096_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are three positive integers $A$, $B$ and $C$ written on a blackboard. E869120 performs the following operation $K$ times:\n\n*   Choose one integer written on the blackboard and let the chosen int...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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