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: Accepted)

using System;
using System.Text;
using System.IO;
using System.Collections.Generic;
using System.Linq;

namespace sandbox
{
    class Program
    {
        static void Main(string[] args)
        {
            var consoleReader = new ConsoleReader(Console.In);
            var N = consoleReader.Int;
            var M = consoleReader.Int;
            var works = consoleReader.Repeat(N).Select(cr => new PartTimeWork { days = cr.Int, pay = cr.Int })
                .Where(w => w.days <= M)
                .OrderBy(w => w.days)
                .ToArray();

            var remaining = new SortedList<int, int>(Comparer<int>.Create((p1, p2) => p2 - p1));
            long pay = 0;
            var i = 0;

            for (int d = 1; d <= M; d++)
            {
                while (i < works.Length && works[i].days <= d)
                {
                    var p = works[i++].pay;
                    if (remaining.ContainsKey(p))
                        ++remaining[p];
                    else
                        remaining.Add(p, 1);
                }

                if (remaining.Count > 0)
                {
                    var first = remaining.First();
                    pay += first.Key;
                    if (first.Value > 1)
                        --remaining[first.Key];
                    else
                        remaining.RemoveAt(0);
                }
            }

            Console.WriteLine(pay);
        }
        struct PartTimeWork
        {
            public override string ToString() => $"days:{days}, pay:{pay}";
            public int days;
            public int pay;
        }
    }

    class ConsoleReader
    {
        private Queue<string> queue = new Queue<string>();
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (queue.Count > 0) return queue.Dequeue();
                var line = textReader.ReadLine().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
                for (int i = 1; i < line.Length; i++) queue.Enqueue(line[i]);
                return line[0];
            }
        }
        public class RepeatReader
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerable<T> Select<T>(Func<ConsoleReader, T> func) { for (int i = 0; i < count; i++) yield return func(cr); }
            public IEnumerable<string> String { get { for (int i = 0; i < count; i++) yield return cr.String; } }
            public IEnumerable<int> Int { get { for (int i = 0; i < count; i++) yield return cr.Int; } }
            public IEnumerable<double> Double { get { for (int i = 0; i < count; i++) yield return cr.Double; } }
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
}