Problem:
Score : 400 points

Problem Statement

There are N one-off jobs available. If you take the i-th job and complete it, you will earn the reward of B_i after A_i days from the day you do it.

You can take and complete at most one of these jobs in a day.

However, you cannot retake a job that you have already done.

Find the maximum total reward that you can earn no later than M days from today.

You can already start working today.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i \leq 10^5

1 \leq B_i \leq 10^4

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
\vdots
A_N B_N

Output

Print the maximum total reward that you can earn no later than M days from today.

Sample Input 1

3 4
4 3
4 1
2 2

Sample Output 1

5

You can earn the total reward of 5 by taking the jobs as follows:

Take and complete the first job today. You will earn the reward of 3 after four days from today.

Take and complete the third job tomorrow. You will earn the reward of 2 after two days from tomorrow, that is, after three days from today.

Sample Input 2

5 3
1 2
1 3
1 4
2 1
2 3

Sample Output 2

10

Sample Input 3

1 1
2 1

Sample Output 3

0

Solution in Ruby (2.3.3) (judge verdict: Accepted)

class PriorityQueue
  attr_reader :size

  def initialize(order: :asc)
    @size = 0
    @nodes = []
  end

  def empty?
    @size.zero?
  end

  def push(node)
    index = size
    @size += 1

    while index > 0
      parent = (index - 1) / 2

      break if @nodes[parent].last <= node.last

      @nodes[index] = @nodes[parent]
      index = parent
    end

    @nodes[index] = node
  end

  alias_method :<<, :push

  def pop
    node = @nodes.first
    root = @nodes[size - 1]
    @size -= 1
    index = 0

    while index * 2 + 1 < @size
      left = 2 * index + 1
      right = left + 1

      if right < size && @nodes[right].last < @nodes[left].last
        left = right
      end

      break if @nodes[left].last >= root.last

      @nodes[index] = @nodes[left]
      index = left
    end

    @nodes[index] = root
    node.first
  end

  def top
    @nodes.first
  end
end

N, M = gets.split.map(&:to_i)

queries = N.times.map { gets.split.map(&:to_i) }

pque_day = PriorityQueue.new
pque_value = PriorityQueue.new

queries.each do |q|
  node = [q, q.first]
  pque_day.push(node)
end

ans = 0

1.upto(M) do |m|
  while !pque_day.empty? && pque_day.top.first.first <= m
    e = pque_day.pop
    pque_value.push([e, -e.last])
  end

  if !pque_value.empty?
    e = pque_value.pop
    ans += e.last
  end
end

puts ans