Jewels

AtCoder

IDnikkei2019_qual_f

Time2000ms

Memory256MB

Difficulty—

There are $N$ jewels, numbered $1$ to $N$. The color of these jewels are represented by integers between $1$ and $K$ (inclusive), and the color of Jewel $i$ is $C_i$. Also, these jewels have specified values, and the value of Jewel $i$ is $V_i$. Snuke would like to choose some of these jewels to exhibit. Here, the set of the chosen jewels must satisfy the following condition: * For each chosen jewel, there is at least one more jewel of the same color that is chosen. For each integer $x$ such that $1 \leq x \leq N$, determine if it is possible to choose exactly $x$ jewels, and if it is possible, find the maximum possible sum of the values of chosen jewels in that case. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq K \leq \lfloor N/2 \rfloor$ * $1 \leq C_i \leq K$ * $1 \leq V_i \leq 10^9$ * For each of the colors, there are at least two jewels of that color. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $C_1$ $V_1$ $C_2$ $V_2$ $:$ $C_N$ $V_N$ [samples]

Samples

Input #1

Output #1

\-1
9
6
14
15

We cannot choose exactly one jewel.
When choosing exactly two jewels, the total value is maximized when Jewel $4$ and $5$ are chosen.
When choosing exactly three jewels, the total value is maximized when Jewel $1, 2$ and $3$ are chosen.
When choosing exactly four jewels, the total value is maximized when Jewel $2, 3, 4$ and $5$ are chosen.
When choosing exactly five jewels, the total value is maximized when Jewel $1, 2, 3, 4$ and $5$ are chosen.

Input #2

Output #2

Input #3

Output #3

\-1
24
-1
46
-1
64
-1
77

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Jewels",
    "description": {
      "content": "There are $N$ jewels, numbered $1$ to $N$. The color of these jewels are represented by integers between $1$ and $K$ (inclusive), and the color of Jewel $i$ is $C_i$. Also, these jewels have specified",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "nikkei2019_qual_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ jewels, numbered $1$ to $N$. The color of these jewels are represented by integers between $1$ and $K$ (inclusive), and the color of Jewel $i$ is $C_i$. Also, these jewels have specified...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments