Various Sushi

AtCoder

IDabc116_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ pieces of sushi. Each piece has two parameters: "kind of topping" $t_i$ and "deliciousness" $d_i$. You are choosing $K$ among these $N$ pieces to eat. Your "satisfaction" here will be calculated as follows: * The satisfaction is the sum of the "base total deliciousness" and the "variety bonus". * The base total deliciousness is the sum of the deliciousness of the pieces you eat. * The variety bonus is $x*x$, where $x$ is the number of different kinds of toppings of the pieces you eat. You want to have as much satisfaction as possible. Find this maximum satisfaction. ## Constraints * $1 \leq K \leq N \leq 10^5$ * $1 \leq t_i \leq N$ * $1 \leq d_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $t_1$ $d_1$ $t_2$ $d_2$ $.$ $.$ $.$ $t_N$ $d_N$ [samples]

Samples

Input #1

Output #1

26

If you eat Sushi $1,2$ and $3$:

*   The base total deliciousness is $9+7+6=22$.
*   The variety bonus is $2*2=4$.

Thus, your satisfaction will be $26$, which is optimal.

Input #2

Output #2

25

It is optimal to eat Sushi $1,2,3$ and $4$.

Input #3

6 5
5 1000000000
2 990000000
3 980000000
6 970000000
6 960000000
4 950000000

Output #3

4900000016

Note that the output may not fit into a $32$\-bit integer type.

API Response (JSON)

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    "name": "Various Sushi",
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      "content": "There are $N$ pieces of sushi. Each piece has two parameters: \"kind of topping\" $t_i$ and \"deliciousness\" $d_i$. You are choosing $K$ among these $N$ pieces to eat. Your \"satisfaction\" here will be ca",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc116_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ pieces of sushi. Each piece has two parameters: \"kind of topping\" $t_i$ and \"deliciousness\" $d_i$. You are choosing $K$ among these $N$ pieces to eat. Your \"satisfaction\" here will be ca...",
      "is_translate": false,
      "language": "English"
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