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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace atc
{
    class MaxHeap<T> where T: IComparable
    {
        private List<T> Array;

        public MaxHeap()
        {
            Array = new List<T>();
        }

        public int Count
        {
            get { return this.Array.Count; }
        }

        public static int Parent(int i)
        {
            return (i-1)/2;
        }

        public static int Left(int i)
        {
            return i*2 + 1;
        }

        public static int Right(int i)
        {
            return i*2 + 2;
        }

        public void Insert(T elem)
        {
            Array.Add(elem);
            int i = Array.Count-1;
            int parent = Parent(i);
            while (i != 0 && Array[i].CompareTo(Array[parent]) > 0) {
                Swap(parent, i);
                i = parent;
                parent = Parent(i);
            }
        }

        private void Heapify(int i)
        {
            int right = Right(i);
            int left  = Left(i);
            int max = i;
            if (right < Count && Array[right].CompareTo(Array[max]) > 0) {
                max = right;
            }
            if (left < Count && Array[left].CompareTo(Array[max]) > 0) {
                max = left;
            }
            if (max != i) {
                Swap(max, i);
                Heapify(max);
            }
        }

        public T PopMax()
        {
            if (Count == 0) {
                return default(T);
            }
            T tmp = Array[0];
            Array[0] = Array[Count-1];
            Heapify(0);
            return tmp;
        }

        private void Swap(int a, int b)
        {
            T tmp = Array[b];
            Array[b] = Array[a];
            Array[a] = tmp;
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            var input1 = Console.ReadLine().Split(' ');
            int n = int.Parse(input1[0]);
            int m = int.Parse(input1[1]);

            var data = new List<int[]>();
            for (int i=0; i<n; i++) {
                var input = Console.ReadLine().Split(' ');
                var d = new int[]{int.Parse(input[0]), int.Parse(input[1])};
                data.Add(d);
            }

            var h = new MaxHeap<int>();
            long sum = 0;

            for (int d=1; d<=m; d++) {
                foreach (var p in data) {
                    if (p[0] == d) {
                        h.Insert(p[1]);
                    }
                }
                sum += h.PopMax();
            }
            Console.WriteLine(sum);
        }
    }
}