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: Wrong Answer)

import java.util.*;

class Albeit {
    final int reward;
    final int days;

    Albeit(int days, int reward) {
        this.days = days;
        this.reward = reward;
    }

    boolean canEarn(int remaining) {
        return remaining > days;
    }
}

class Solver {
    void solve(Scanner sc) {
        int N = sc.nextInt();
        int M = sc.nextInt();
        Queue<Albeit> queue = new PriorityQueue<>(Comparator.comparingInt((Albeit a) -> a.reward).reversed().thenComparingInt(a -> a.days));
        for (int i = 0; i < N; i++) {
            queue.add(new Albeit(sc.nextInt(), sc.nextInt()));
        }
        int sum = 0;
        for (int i = 2; i <= M + 1; i++) {
            Albeit peek = queue.poll();
            if (peek == null) break;
            while (peek != null && !peek.canEarn(i)) {
                peek = queue.poll();
            }
            if (peek == null) break;
            sum += peek.reward;
        }
        System.out.println(sum);
    }
}

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

        new Solver().solve(in);

        in.close();
    }
}