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: Wrong Answer)

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

AB = []
N.times do |i|
  AB[i] = gets.chomp.split(' ').map(&:to_i)
end

group_by_day = AB.group_by{|v|v[0]}.each

day_reward = {}
group_by_day.each do |k, v| 
  day_reward[k] = v.map{|m| m[1]}
end

print day_reward

@days = Array.new(M+1, 0)

# print "\n"
# print @days
# print "\n"
day_reward.each do |d, r|
  break if d > M
  target_date = d
  r.sort.reverse.each do |reward|
    
    # すでにある値との比較
    while (@days[target_date] && @days[target_date] >= reward)
      target_date += 1
    end

    break if target_date > M

    if (@days[target_date] > 0) 
      @days[target_date + 1] = @days[target_date]
    end
    @days[target_date] = reward
    target_date += 1
  end
end

print @days

@output = 0
@days.each do |v|
  @output += v
end

puts @output