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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    int M = scanner.nextInt();
    Job[] jobs = new Job[N];
    for (int i = 0; i < N; i++) jobs[i] = new Job(scanner.nextInt(), scanner.nextInt());
    Arrays.sort(jobs, Comparator.comparingInt(j -> j.due));

    int ans = 0;
    int j = 0;
    PriorityQueue<Job> pq = new PriorityQueue<>();
    for (int i = 1; i <= M; i++) {
      while (j < N && jobs[j].due <= i) pq.add(jobs[j++]);
      if (!pq.isEmpty()) ans += pq.poll().reward;
    }
    System.out.println(ans);
  }

  private static class Job implements Comparable<Job> {
    private final int due;
    private final int reward;

    private Job(int due, int reward) {
      this.due = due;
      this.reward = reward;
    }

    @Override public int compareTo(Job job) {
      return job.reward - reward;
    }
  }
}