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.chomp.split(" ").map(&:to_i)

ret = Array.new(m, 0) # [最終日, .... , 最初の日]

inputs = []
(0..(n-1)).each do |i|
    a,b=gets.chomp.split(" ").map(&:to_i)
    inputs[i] = [a, b]
end

inputs = inputs.sort {|a, b| b[1] <=> a[1] }

path = (0..m-1).to_a
inputs.each do |input|
    a = input[0]
    b = input[1]
    if m >= a
        target = a-1
        while true do
            target = path[target]
            break if target == nil || target == path[target]
        end

        next if target == nil
        ret[target] = b
        break unless ret.include?(0)
        if target + 1 == m
            path[target] = nil
        else
            path[target] = target + 1
        end
    end
end

puts ret.reduce(&:+)