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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var line = consoleReader.Split.Int;
            var N = line[0];
            var M = line[1];
            var works = consoleReader.Repeat(N).SplitInt.Select(PartTimeWork.FromArray)
                .Where(w => w.days <= M)
                .OrderBy(w => w.days)
                .ToArray();

            var remainingWorks = new SortedCollection<PartTimeWork>(Comparer<PartTimeWork>.Create(
                (p1, p2) => p2.pay - p1.pay
                ));
            long pay = 0;
            var i = 0;

            for (int d = 1; d <= M; d++)
            {
                while (i < works.Length && works[i].days <= d)
                {
                    remainingWorks.Add(works[i++]);
                }

                if (remainingWorks.Count > 0)
                {
                    pay += remainingWorks[0].pay;
                    remainingWorks.RemoveAt(0);
                }
            }

            return pay;
        }
        struct PartTimeWork
        {
            public static PartTimeWork FromArray(int[] l) => new PartTimeWork
            {
                days = l[0],
                pay = l[1]
            };
            public override string ToString() => $"days:{days}, pay:{pay}";
            public int days;
            public int pay;
        }
        class SortedCollection<T> : List<T>
        {
            private IComparer<T> Comparer { get; }
            public SortedCollection() : this(Comparer<T>.Default) { }
            public SortedCollection(IComparer<T> comparer) { this.Comparer = comparer; }
            public new int Add(T item)
            {
                if (this.Count == 0)
                {
                    base.Add(item);
                    return 0;
                }

                int start = 0;
                int end = this.Count;
                while (start != end)
                {
                    var half = (start + end) / 2;
                    if (Comparer.Compare(item, this[half]) < 0)
                    {
                        end = half;
                    }
                    else
                    {
                        start = half + 1;
                    }
                }

                Insert(start, item);
                return start;
            }
        }


        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader()).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        #endregion
    }

#pragma warning disable
    public class ConsoleReader { public class SplitLine { string[] splited; public SplitLine(string line) { splited = line.Split(); } public string[] String => splited.ToArray(); public int[] Int => splited.Select(int.Parse).ToArray(); public long[] Long => splited.Select(long.Parse).ToArray(); public ulong[] ULong => splited.Select(ulong.Parse).ToArray(); public double[] Double => splited.Select(double.Parse).ToArray(); } public class RepeatLine { ConsoleReader reader; int num; public RepeatLine(ConsoleReader reader, int num) { this.reader = reader; this.num = num; } public IEnumerable<string> String { get { for (int i = 0; i < num; i++) yield return reader.String; } } public IEnumerable<int> Int { get { for (int i = 0; i < num; i++) yield return reader.Int; } } public IEnumerable<long> Long { get { for (int i = 0; i < num; i++) yield return reader.Long; } } public IEnumerable<string[]> SplitString { get { for (int i = 0; i < num; i++) yield return reader.Split.String; } } public IEnumerable<int[]> SplitInt { get { for (int i = 0; i < num; i++) yield return reader.Split.Int; } } } public virtual string String => Console.ReadLine(); public int Int => int.Parse(String); public long Long => long.Parse(String); public ulong ULong => ulong.Parse(String); public double Double => double.Parse(String); public SplitLine Split => new SplitLine(String); public RepeatLine Repeat(int count) => new RepeatLine(this, count); }
}