D - Various Sushi

Score : $400$ points

Problem Statement

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:

$N$ $K$

$t_1$ $d_1$

$t_2$ $d_2$

$.$

$.$

$.$

$t_N$ $d_N$

Output

Print the maximum satisfaction that you can obtain.

5 3
1 9
1 7
2 6
2 5
3 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.

7 4
1 1
2 1
3 1
4 6
4 5
4 5
4 5

25

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

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

4900000016

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