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: Runtime Error)

def merge (x,y)
    if x.empty? then
        y
    else
        i = 0
        while e = y.shift do
            while x[i] < e do
                i += 1
            end
            x[i,0] = e 
            i += 1

            if i == x.length then 
                x.concat(y)
                break
            end
        end
        x
    end
end

n, m = gets.split.map!(&:to_i)

ab = Hash.new
n.times do 
    a,b = gets.split.map(&:to_i)
    if ab[a] then
        ab[a] << b
    else
        ab[a] = [b]
    end
end
ab = ab.to_a.sort!{|x,y| x[0] <=> y[0]} << [m+1,[0]]

ans = 0
queue = Array.new
(1..m).each do |day|
    while ab[0][0] <= day do
        queue = merge(queue,ab.shift[1].sort!)
    end
    if queue != [] then
        ans += queue.pop 
    end
    p [day,ans,queue]
    p ab
end

puts ans