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: Accepted)

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

job = []

for i in 1..n do
    job.push(gets.chomp.split(" ").map(&:to_i))
end
job.sort! {|a,b| (a[0] <=> b[0]).nonzero? || (b[0] <=> a[0])}

# p job

sum = 0
stack = []
for i in 1..m do
    if ! job.empty?
        while job[0][0] <= i
            tar = job.shift
            if stack.empty?
                stack.push(tar)
            else
                head = 0
                tail = stack.size-1
                mid = ((head+tail)/2.0).ceil
                while head <= tail
                    if tar[1] == stack[mid][1]
                        break
                    elsif tar[1] < stack[mid][1]
                        head = mid + 1
                    else
                        tail = mid - 1
                    end
                    mid = ((head+tail)/2.0).ceil
                end
                if mid > stack.size
                    stack.push(tar)
                else 
                    stack.insert(mid,tar)
                end
            end
            if job.empty?
                break
            end
        end
    end
    if ! stack.empty?
        tar = stack.shift
        sum += tar[1]
    end
    # print i," ", stack,"\n"
end

p sum