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;

class Procon {
    public Procon () { }
    static void Main (string[] agrs) {
        new Procon ().Do ();
    }

    Scanner cin;

    public void Do () {
        cin = new Scanner ();
        int N = cin.nextInt ();
        int M = cin.nextInt ();
        List<Tuple<int, int>> work = new List<Tuple<int, int>> ();

        for (int i = 0; i < N; i++) {
            work.Add (Tuple.Create (cin.nextInt (), cin.nextInt ()));
        }

        work.Sort ((a, b) => {
            if (a.Item1 == b.Item1) {
                return b.Item2 - a.Item2;
            }
            return b.Item1 - a.Item1;
        });

        List<int> ret = new List<int> ();

        long ans = 0;
        int cur = 0;
        int cur2 = 0;
        for (int i = 0; i < N; i++) {
            if (cur + work[i].Item1 <= M) {
                ans += work[i].Item2;
                cur++;
                ret.Add (work[i].Item2);
                ret.Sort ();
            } else {
                if (ret.Count == 0) {
                    continue;
                }
                if (ret[cur2] < work[i].Item2 && cur + work[i].Item1 <= M + 1) {
                    ans -= ret[cur2];
                    ans += work[i].Item2;
                    cur2++;
                }
            }
        }

        Console.WriteLine (ans);
    }
}

class Scanner {
    string[] s;
    int i;
    int max_i;

    public Scanner () {
        s = new string[0];
        max_i = 0;
        i = 0;
    }

    public string nextString () {
        if (i >= s.Length) {
            s = Console.ReadLine ().Split (' ');
            max_i = s.Length;
            i = 0;
            if (max_i == 0) {
                return "";
            }
            return s[i++];
        } else {
            return s[i++];
        }
    }

    public int nextInt () {
        return int.Parse (nextString ());
    }

    public long nextLong () {
        return long.Parse (nextString ());
    }

    public double nextDouble () {
        return double.Parse (nextString ());
    }

    public string[] arrayString () {
        return Console.ReadLine ().Split (' ');
    }

    public int[] arrayInt () {
        string[] str = Console.ReadLine ().Split (' ');
        int[] array = new int[str.Length];
        for (int i = 0; i < str.Length; i++) {
            array[i] = int.Parse (str[i]);
        }
        return array;
    }

    public long[] arrayLong () {
        string[] str = Console.ReadLine ().Split (' ');
        long[] array = new long[str.Length];
        for (int i = 0; i < str.Length; i++) {
            array[i] = long.Parse (str[i]);
        }
        return array;
    }

    public double[] arrayDouble () {
        string[] str = Console.ReadLine ().Split (' ');
        double[] array = new double[str.Length];
        for (int i = 0; i < str.Length; i++) {
            array[i] = double.Parse (str[i]);
        }
        return array;
    }
}