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

namespace ABC137D
{
    class Program
    {
        public static void Solve(Input input)
        {
            var n = input.NextInt();
            var m = input.NextInt();

            var a = new int[n];
            var b = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = input.NextInt();
                b[i] = input.NextInt();
            }

            // 最大でm件のバイトしかできない
            // 最後の日は日数1のバイトしかできない
            // その前の日は日数2、
            // よって、日数1以下で最大のもの、日数2以下で最大のもの……となる

            Array.Sort(a, b);
            long pay = 0;
            var d = 0;
            var pq = new PriorityQueue<int>(8, false);
            for (int i = 0; i < m; i++)
            {
                for (; d < n && a[d] <= i + 1; d++)
                {
                    pq.Push(b[d]);
                }

                if (pq.Any()) { pay += pq.Pop(); }
            }

            Console.WriteLine(pay);
        }

        /// <summary>
        /// 優先度付きキュー
        /// デフォルトは昇順にソートされていて、小さい値から取り出される
        /// </summary>
        /// <typeparam name="T"></typeparam>
        class PriorityQueue<T> where T : IComparable<T>
        {
            readonly List<T> Heap;
            readonly Func<T, T, bool> compare;

            public PriorityQueue(int capacity, bool isMinHeap = true)
            {
                this.Heap = new List<T>(capacity);

                if (isMinHeap)
                {
                    compare = (x, y) => x.CompareTo(y) < 0;
                }
                else
                {
                    compare = (x, y) => x.CompareTo(y) > 0;
                }
            }

            public PriorityQueue() : this(0) { }

            /// <summary>
            /// 要素追加
            /// </summary>
            /// <param name="item"></param>
            public void Push(T item)
            {
                var n = Heap.Count();
                Heap.Add(item);

                while (n > 0)
                {
                    var parent = (n - 1) / 2;
                    if (compare(Heap[parent], item)) break;

                    Heap[n] = Heap[parent];
                    n = parent;
                }

                Heap[n] = item;
            }

            /// <summary>
            /// 先頭の値取得し削除する
            /// </summary>
            /// <returns></returns>
            public T Pop()
            {
                if (!Heap.Any())
                {
                    throw new Exception();
                }
                var item = Heap[0];
                var last = Heap.Last();

                var n = Heap.Count() - 1;
                var parent = 0;
                var child = 2 * parent + 1;
                while (child < n)
                {
                    if (child + 1 < n && compare(Heap[child + 1], Heap[child]))
                    {
                        child++;
                    }

                    if (compare(last, Heap[child])) break;

                    Heap[parent] = Heap[child];
                    parent = child;
                    child = 2 * parent + 1;
                }

                Heap[parent] = last;
                Heap.RemoveAt(n);

                return item;
            }

            /// <summary>
            /// 先頭の値取得（削除はしない）
            /// </summary>
            /// <returns></returns>
            public T Peek()
            {
                if (!this.Heap.Any())
                {
                    throw new Exception();
                }

                return this.Heap[0];
            }

            /// <summary>
            /// ヒープに格納されているアイテム数
            /// </summary>
            /// <returns></returns>
            public int Count() => this.Heap.Count();

            /// <summary>
            /// 一つでの値が格納されているか
            /// </summary>
            /// <returns></returns>
            public bool Any() => this.Heap.Any();
        }

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // そのときにTLEするのはアルゴリズムが悪いせいだし、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();

            // 仮想的に標準入力をセットする
            // テスト入力したまま提出することがままあるので……
#if DEBUG
            input.SetText("");
#endif

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
        static readonly int[] dx = { 1, 0, -1, 0 };
        static readonly int[] dy = { 0, 1, 0, -1 };
        /// <summary> 左上が原点 </summary>
        static readonly char[] dir = { 'R', 'U', 'L', 'D' };
#pragma warning restore CS0414

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            readonly StreamReader sr;
            readonly Queue<string> queue;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            public Input(string path = "")
            {
                queue = new Queue<string>();

                if (string.IsNullOrEmpty(path)) { sr = new StreamReader(Console.OpenStandardInput()); }
                else { sr = new StreamReader(path); }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                    SetText(item);
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public bool SetText(string s)
            {
                if (string.IsNullOrEmpty(s)) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                    queue.Enqueue(elem);

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            public bool Any() => queue.Any() || Read();

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            bool Read()
            {
                if (!SetText(sr.ReadLine())) return false;

                if (!queue.Any()) return Read();

                return queue.Any();
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            public string Next()
            {
                if (!queue.Any() && !Read()) return "";

                return queue.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            bool Accumulate(int n)
            {
                while (queue.Count() < n)
                    if (!Read()) return false;

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!Accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(queue.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            public static T[][] Create2DArray<T>(int d1, int d2, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                    Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}