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.strip.split(' ').map(&:to_i)
ABS = readlines.map {|line| line.split(' ').map(&:to_i)}

money = 0
left_day = M

jobs = ABS.group_by{|job| job[0]}
M.times do |i|
  today = i + 1
  target_index = nil
  current = 0
  today.times do |d|
    s = today - d
    unless jobs[s].nil? || jobs[s].size == 0
      jobs[s].sort_by! {|x| -x[1]}
      if current < jobs[s][0][1]
        current = jobs[s][0][1] 
        target_index = s
      end
    end
  end
  money += current
  jobs[target_index].delete_at(0) if target_index
end

puts money