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 Program
{
    public static void Main()
    {
        var nm = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
        var N = nm[0];
        var M = nm[1];
        var list = new List<int[]>();
        var listCount = 0;
        for (int i = 0; i < N; ++i)
        {
            var ab = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
            if (M < ab[0]) continue;
            list.Add(new int[] { ab[0], ab[1] });
            listCount++;
        }
        list = list.OrderBy(x => x[0]).ToList();
        var tempList = new List<int>();
        var index = 0;
        var ans = 0;
        if(1 <= listCount)
        {
            for (int i = 0; i < M; ++i)
            {
                while (index <= listCount - 1 && list[index][0] <= i + 1)
                {
                    var ins = LowerBound(list[index][1], tempList);
                    tempList.Insert(ins, list[index][1]);
                    index++;
                }
                if (1 <= tempList.Count())
                {
                    var n = tempList.Last();
                    ans += n;
                    tempList.Remove(n);
                }
            }
        }
        Console.WriteLine(ans);
    }

    static int LowerBound(long value, List<int> array)
    {
        var low = 0;
        var high = array.Count();
        
        while (low < high)
        {
            var middle = (high + low) / 2;
            if (value <= array[middle]) high = middle;
            else low = middle + 1;
        }
        return low;
    }
}