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 System.Text;
using System.Threading.Tasks;
using System.Diagnostics;

static class CodeJam
{
    struct Work
    {
        public readonly int A;
        public readonly int B;
        public Work(string[] args)
        {
            A = int.Parse(args[0]);
            B = int.Parse(args[1]);
        }
    }

    static int Solve(int N, int M, Work[] works)
    {
        var ranges = new List<Tuple<int, int>> { new Tuple<int, int>(0, M) };
        int sum = 0;
        for (int i = 0; i < N && ranges.Count > 0; ++i)
        {
            int n = M - works[i].A;
            for (int j = 0; j < ranges.Count; ++j)
            {
                int S = ranges[j].Item1;
                int E = ranges[j].Item2;
                if (S <= n)
                {
                    sum += works[i].B;
                    if (n == S)
                    {
                        if (S + 1 < E) { ranges.Add(new Tuple<int, int>(S + 1, E)); }
                    }
                    else if (n >= E - 1)
                    {
                        if (S < E - 1) { ranges.Add(new Tuple<int, int>(S, E - 1)); }
                    }
                    else
                    {
                        ranges.Add(new Tuple<int, int>(S, n));
                        ranges.Add(new Tuple<int, int>(n + 1, E));
                    }
                    ranges.RemoveAt(j);
                    break;
                }
            }
            ranges.Sort((x, y) => y.Item1.CompareTo(x.Item1));
        }
        return sum;
    }

    static void Main(string[] args)
    {
        int[] V = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int N = V[0], M = V[1];
        var works = new Work[N];
        for (int i = 0; i < N; ++i) { works[i] = new Work(Console.ReadLine().Split()); }
        Console.WriteLine(Solve(N, M, works.OrderByDescending(work => work.B).ThenByDescending(work => work.A).ToArray()));
    }
}