10534: ABC116 —— D - Various Sushi
[Creator : ]
Description
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.
- 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.
Input
Input is given from Standard Input in the following format:
```
$N$ $K$
$t_1$ $d_1$
$t_2$ $d_2$
$.$
$.$
$.$
$t_N$ $d_N$
```
```
$N$ $K$
$t_1$ $d_1$
$t_2$ $d_2$
$.$
$.$
$.$
$t_N$ $d_N$
```
Output
Print the maximum satisfaction that you can obtain.
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.
- $1 \leq t_i \leq N$
- $1 \leq d_i \leq 10^9$
- All values in input are integers.
Sample 1 Input
5 3
1 9
1 7
2 6
2 5
3 1
Sample 1 Output
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.
Sample 2 Input
7 4
1 1
2 1
3 1
4 6
4 5
4 5
4 5
Sample 2 Output
25
It is optimal to eat Sushi 1,2,3 and 4.
Sample 3 Input
6 5
5 1000000000
2 990000000
3 980000000
6 970000000
6 960000000
4 950000000
Sample 3 Output
4900000016