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 Ruby (2.3.3) (judge verdict: Accepted)

require 'set'

N, K = gets.split.map &:to_i
Sushis = [*0...N].map{ gets.split.map &:to_i }


# Editorialを参考にした解法
# 1. まずSushisを美味しさ基礎点順に降順ソートし、先頭からK個選ぶ
Delicious_Sushis = Sushis.sort_by{|sushi| -sushi[1]}
selected_Sushis = Delicious_Sushis.take(K)
selected_Sushis_Point = selected_Sushis.inject(0){|sum, sushi| sum + sushi[1]}
num_selected_Sushis = selected_Sushis.size
selected_Groups_Set = selected_Sushis.map{|sushi| sushi[0]}.to_set
num_selected_Groups = selected_Groups_Set.size

# 2. selected_Sushisに含まれない種類のSushi Kindそれぞれについて、最大値の美味しさポイントを持つSushiを1つずつ取り出す
Unselected_Sushi_Groups = Delicious_Sushis.drop(K).group_by{|sushi| sushi[0]}
Unselected_but_Delicious_Sushis = Unselected_Sushi_Groups.values.map{|sushi_group| sushi_group.sort_by{|sushi| -sushi[1]}.first}

# 3. selected_Sushisについて、2のUnselected_but_Delicious_Sushisと交換可能なSushiについて求める
Changeable_Sushi = selected_Sushis.group_by{|sushi| sushi[0]}.values.select{|sushi_group| sushi_group.size >= 2}.map{|sushi_group| sushi_group.sort_by{|sushi| sushi[1]}.map{|sushi| sushi[1]}.take(sushi_group.size - 1)}.flatten.sort

# Unselected_but_Delicious_Sushisについて、Changeable_Sushiに含まれるsushiと順番に交換して合計点を求める

max_point = selected_Sushis_Point + num_selected_Groups**2

#p "selected_Sushis_Point: #{selected_Sushis_Point}, num_selected_Groups: #{num_selected_Groups}, max_point: #{max_point}"
#p "Unselected_but_Delicious_Sushis: #{Unselected_but_Delicious_Sushis}"
#p "Changeable_Sushi: #{Changeable_Sushi}"
#puts "------------------------------"

num_changed_sushi = 0
for i in 0...Unselected_but_Delicious_Sushis.size do
	break if Changeable_Sushi.size <= num_changed_sushi

	unselected_sushi = Unselected_but_Delicious_Sushis[i]
	next if selected_Groups_Set.include?(unselected_sushi[0])

	changeable_sushi = Changeable_Sushi[num_changed_sushi]

	num_selected_Groups += 1
	selected_Sushis_Point += unselected_sushi[1] - changeable_sushi
	new_point = selected_Sushis_Point + num_selected_Groups**2

	max_point = [max_point, new_point].max
	#p "unselected_sushi: #{unselected_sushi}"
	#p "changeable_sushi: #{changeable_sushi}"
	#p "num_selected_Groups: #{num_selected_Groups}"
	#p "max_point: #{max_point}"
	#p "Changeable_Sushi.size: #{Changeable_Sushi.size} i: #{i}"

	num_changed_sushi += 1
end

p max_point