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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var nm = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var n = nm[0];
        var m = nm[1];
        var seqW = new Tuple<int, int>[n];
        for (int i = 0; i < seqW.Length; ++i)
        {
            var ab = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            seqW[i] = Tuple.Create(ab[0], -ab[1]);
        }

        Array.Sort(seqW);

        var sum = 0L;
        var works = new SortedSet<Tuple<int, int>>();
        var d = 1;
        for (int i = 0; i < seqW.Length; ++i)
        {
            if (d > m || seqW[i].Item1 > m)
            {
                break;
            }

            works.Add(Tuple.Create(seqW[i].Item2, seqW[i].Item1));
            var min = works.Min;
            if (seqW[i].Item1 < d)
            {
                continue;
            }
            while (d <= min.Item2)
            {
                ++d;
            }

            sum += min.Item1;
            works.Remove(min);
        }

        Console.WriteLine(-sum);
    }
}