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: Time Limit Exceeded)

N,M = gets.split.map(&:to_i)
jobs = {}
N.times do
  a,b = gets.split.map(&:to_i)
  if jobs[a].nil?
    jobs[a] = [b]
  else
    jobs[a].push(b)
  end
end
jobs = jobs.map{|k,v| [k, v.sort{|a, b| b <=> a }]}.to_h

sum = 0
can_jobs = []
(1..M).each do |i|
  unless jobs[i].nil?
    jobs[i].each do |x|
      if can_jobs.empty?
        can_jobs.push x
      else
        idx = [*can_jobs.each_with_index].bsearch{|y,_| y<= x}&.last
        if idx.nil?
          can_jobs.push x
        else
          can_jobs.insert(idx, x)
        end
      end
    end
  end
  sum += can_jobs.shift unless can_jobs.empty?
end

puts sum