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 (2.7.1) (judge verdict: Accepted)

#!/usr/bin/env ruby

require 'set'

class Hash
  def push(key, value)
    self[key] = [] if self[key] == nil
    self[key].push(value)
  end
end

class Array
  def lower_bound(value)
    left = -1;
    right = self.length;
    while left + 1 < right
      mid = left + (right - left) / 2;
      if self[mid] >= value
        right = mid
      else
        left = mid
      end
    end
    right
  end

  def unique
    res = [self.first]
    each_cons(2) do |a, b|
      if a != b
        res.push(b)
      end
    end
    res
  end
end

def get_ints
  gets.chomp.split.map(&:to_i)
end

def get_ints_minus_one
  get_ints.map { |x| x - 1 }
end

def get_int
  gets.chomp.to_i
end

N, K = get_ints
TD = []
N.times do |i|
  TD[i] = [i] + get_ints
end

TD.sort! { |a, b| a[2] <=> b[2] }.reverse!

if K == 1
  puts TD[0][2] + 1
else
  sets = Array.new(N+1) { Set.new }
  kind_bonus = Set.new
  points = 0

  TD[0...K].each.with_index do |(i, t, d)|
    sets[t].add(i)
    kind_bonus.add(t)
    points += d
  end


  max = points + kind_bonus.length ** 2

  left = K-1
  right = K

  while left >= 0
    i, t, d = TD[left]
    # 重複しているものを低い値から探す
    if sets[t].length > 1
      # 重複しているので、これを除いた新しい種類の最大のものを探す
      while right < N
        right_i, right_t, right_d = TD[right]
        unless kind_bonus.include?(right_t)
          points += right_d - d
          kind_bonus.add(right_t)
          sets[t].delete(i)
          sets[right_t].add(right_i)
          stock = points + kind_bonus.length ** 2
          max = stock if stock > max
          break
        end
        right += 1
      end
    end
    left -= 1
  end

  puts max
end