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.Generic;

class Heap<T> where T : IComparable
{
    public HeapNode<T> top;

    public void push(T val)
    {
        top = HeapNode<T>.meld(top, new HeapNode<T>(val));
    }

    public T pop()
    {
        T ret = top.val;
        top = HeapNode<T>.meld(top.r, top.l);
        return ret;
    }

    public void merge(Heap<T> h2)
    {
        top = HeapNode<T>.meld(top, h2.top);
    }

    public class HeapNode<NT> where NT : IComparable
    {
        public HeapNode<NT> l, r;
        public NT val;

        public HeapNode(NT _val)
        {
            val = _val;
        }

        public static HeapNode<NT> meld(HeapNode<NT> a, HeapNode<NT> b)
        {
            if (a == null) return b;
            if (b == null) return a;
            if (b.val.CompareTo(a.val) > 0)
            {
                HeapNode<NT> temp = a;
                a = b;
                b = temp;
            }
            a.r = meld(a.r, b);
            HeapNode<NT> temph = a.l;
            a.l = a.r;
            a.r = temph;
            return a;
        }
    }
}

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

        var array = new Tuple<int, int>[n];

        for (int i = 0; i < n; i++)
        {
            var ab = Console.ReadLine().Split();
            var a = int.Parse(ab[0]);
            var b = int.Parse(ab[1]);
            array[i] = Tuple.Create(a, b);
        }

        Array.Sort(array);

        var heap = new Heap<int>();
        var index = 0;
        var ans = 0;

        for (int i = 1; i <= m; i++)
        {
            while (index < n && array[index].Item1 <= i)
            {
                heap.push(array[index].Item2);
                index++;
            }

            if (heap.top != null) ans += heap.pop();
        }

        Console.WriteLine(ans);
    }
}