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: Runtime Error)

class Heap
  attr_reader :size

  def initialize
    @heap = []
    @size = 0
  end

  def add(n)
    i = @size
    while i > 0 do
      parent_index = (i - 1) / 2
      break if n >= @heap[parent_index]

      @heap[i] = @heap[parent_index]
      i = parent_index
    end

    @heap[i] = n
    @size += 1
  end

  def pop
    min = @heap[0]
    @size -= 1
    n = @heap[@size]
    i = 0
    while i * 2 + 1 < @size do
      child_index1 = i * 2 + 1
      child_index2 = i * 2 + 2
      if child_index2 < @size && @heap[child_index2] < @heap[child_index1]
        child_index1 = child_index2
      end
      break if @heap[child_index1] >= n

      @heap[i] = @heap[child_index1]
      i = child_index1
    end
    @heap[i] = n
    min
  end

  def min; @heap[0] end
  def values; @heap.first(@size) end
  def inspect; values end
end

N, K = gets.split(' ').map(&:to_i)
sushis = []
N.times do
  t, d = gets.split(' ').map(&:to_i) # t: ネタ, d: おいしさ
  sushis << {
    type: t,
    oisisa: d,
  }
end

sushis.sort_by! { |sushi| -sushi[:oisisa] }
types_count = sushis.map { |sushi| sushi[:type] }.uniq.size

sushi_heaps = Array.new(N + 1) { Heap.new }
K.times.map { sushis.shift }.each do |sushi|
  sushi_heaps[sushi[:type]].add(sushi[:oisisa])
end
current_types_count = sushi_heaps.count { |sushi_heap| sushi_heap.size > 0 }

def calc_points(sushi_heaps)
  sushi_heaps.count { |sushi_heap| sushi_heap.size > 0 } ** 2 + sushi_heaps.inject(0) { |sum, sushi_heap| sum + sushi_heap.values.inject(:+).to_i }
end

max_points = calc_points(sushi_heaps)
current_types_count.upto(types_count) do
  min_i = nil
  min_value = Float::INFINITY
  sushi_heaps.each_with_index do |sushi_heap, i|
    if sushi_heap.size > 1 && sushi_heap.min < min_value
      min_i = i
      min_value = sushi_heap.min
    end
  end
  break if min_i.nil?

  sushi_heaps[min_i].pop
  sushi = sushis.shift
  while sushi_heaps[sushi[:type]].size > 0
    sushi = sushis.shift
  end
  sushi_heaps[sushi[:type]].add(sushi[:oisisa])

  max_points = [max_points, calc_points(sushi_heaps)].max
end

puts max_points