Red and Blue Lamps

AtCoder

IDabc218_h

Time2000ms

Memory256MB

Difficulty—

There are $N$ lamps numbered $1$ through $N$ arranged in a row. You are going to light $R$ of them in red and $N-R$ in blue. For each $i=1,\ldots,N-1$, a reward of $A_i$ is given if Lamp $i$ and Lamp $i+1$ light up in different colors. Find the maximum total reward that can be obtained by efficiently deciding the colors of the lamps. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1 \leq R \leq N-1$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $R$ $A_1$ $A_2$ $\ldots$ $A_{N-1}$ [samples]

Samples

Input #1

6 2
3 1 4 1 5

Output #1

11

Lighting up Lamps $3, 5$ in red and Lamps $1, 2, 4, 6$ in blue yields a total reward of $A_2+A_3+A_4+A_5=11$.
You cannot get any more, so the answer is $11$.

Input #2

7 6
2 7 1 8 2 8

Output #2

10

Lighting up Lamps $1, 2, 3, 4, 5, 7$ in red and Lamp $6$ in blue yields a total reward of $A_5+A_6=10$.

Input #3

11 7
12345 678 90123 45678901 234567 89012 3456 78901 23456 7890

Output #3

46207983

API Response (JSON)

{
  "problem": {
    "name": "Red and Blue Lamps",
    "description": {
      "content": "There are $N$ lamps numbered $1$ through $N$ arranged in a row. You are going to light $R$ of them in red and $N-R$ in blue. For each $i=1,\\ldots,N-1$, a reward of $A_i$ is given if Lamp $i$ and Lamp ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc218_h"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ lamps numbered $1$ through $N$ arranged in a row. You are going to light $R$ of them in red and $N-R$ in blue.\nFor each $i=1,\\ldots,N-1$, a reward of $A_i$ is given if Lamp $i$ and Lamp ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments