Problem:
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.

Sample Input 1

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

Sample 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.

Sample Input 2

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

Sample Output 2

25

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

Sample Input 3

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

Sample Output 3

4900000016

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

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d%d", $N, $K);
for($i = 0; $i < $N; $i++){
    fscanf(STDIN, "%d%d", $t[$i], $d[$i]);
}
array_multisort($d, SORT_DESC, $t);

//美味しい寿司から食べてみる
$sum = 0;
for($i = 0; $i < $K; $i++){
    $sum += $d[$i];
    $map[$t[$i]][] = $d[$i];
}
//食べなかったのも残しておく
for($i = $K; $i < $N; $i++){
    $map2[$t[$i]][] = $d[$i];
}

//美味しさは$sum 種類数は count($map);
$kinds = count($map);
$max = $sum + $kinds**2;

//同じ種類を2個以上食べている場合、まずいほうから順に諦めていけばよい。ただし0個になるのは困る。
//種類Aを3個、種類Bを2個食べていた場合は、種類Aから2個、種類Bから1個は諦めていいよね
$mazuiArray = [];
foreach($map as $kind => &$array){
    sort($array);//不味いのから並べる
    $limit = count($array) - 1;
    for($i = 0; $i < $limit; $i++){
        $mazuiArray[] = $array[$i];
    }
}
//種類を区別せず、不味いもの総合ランキングを作る
sort($mazuiArray);

//選ばれていない種類の寿司の旨さトップを抽出
$umaiArray = [];
for($i = 1; $i <= $N; $i++){
    if(isset($map[$i]))continue;//選ばれている種類の寿司はもうため
    if(isset($map2[$i])){//選ばれてない種別の寿司が存在したら、一番うまいものだけ食べてみよう
        $umaiArray[] = max($map2[$i]);
    }
}
rsort($umaiArray);
$maxSwap = min(count($mazuiArray), count($umaiArray));
for($i = 0; $i < $maxSwap; $i++){
    $kinds++;
    $sum -= $mazuiArray[$i];
    $sum += $umaiArray[$i];
    $score = $sum + $kinds**2;
    $max = max($max, $score);
}
echo $max;