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;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var line1 = Console.ReadLine().Split(' ');
        var n = int.Parse(line1[0]);
        var m = int.Parse(line1[1]);

        var list = new List<int[]>();
        for (var i = 0; i < n; i++)
        {
            var line = Console.ReadLine().Split(' ');
            var val = new int[2];
            val[0] = int.Parse(line[0]);
            val[1] = int.Parse(line[1]);


            if (val[0] > m) continue;
            list.Add(val);
        }

        long ret = 0;
        var targetlist = new PriorityQueue<int>();
        for (var i = 1; i <= m; i++)
        {
            foreach (var v in list.Where(v => v[0] == i))
            {
                targetlist.Push(v[1]);
            }

            if (targetlist.Size() == 0) continue;

            ret += targetlist.Pop();
        }
        Console.Write(ret);
    }
}

public class PriorityQueue<T> where T : IComparable<T>
{
    List<T> heap;

    public PriorityQueue()
    {
        heap = new List<T>();
    }

    public void Push(T value)
    {
        heap.Add(value);
        var node = heap.Count - 1;
        while (node != 0)
        {
            var parent = (node - 1) / 2;
            if (heap[parent].CompareTo(heap[node]) < 0)
            {
                var tmp = heap[node];
                heap[node] = heap[parent];
                heap[parent] = tmp;
            }
            node = parent;
        }
    }

    public T Pop()
    {
        var last = heap.Count - 1;
        var ret = heap[0];

        heap[0] = heap[last];
        heap.RemoveAt(last);

        var node = 0;
        last = heap.Count - 1;
        var child = node * 2 + 1;
        while (child < last)
        {
            if ((child + 1 <= last) && (heap[child].CompareTo(heap[child + 1]) < 0))
            {
                child++;
            }
            if (heap[node].CompareTo(heap[child]) < 0)
            {
                var tmp = heap[node];
                heap[node] = heap[child];
                heap[child] = tmp;
            }
            node = child;
            child = 2 * node + 1;
        }

        return ret;
    }

    public int Size()
    {
        return heap.Count;
    }

}