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;
using System.Linq;
using System.Text;

namespace ABC137
{
    class Program4C
    {
        static void Main()
        {
            var input = Console.ReadLine().Split(' ').Select(int.Parse);
            var N = input.First();
            var M = input.Skip(1).First();
            var list = new int[N + 1][];
            for (int i = 0; i < N; i++)
                list[i] = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            list[N] = new int[] { int.MaxValue, 0 };

            Array.Sort(list, Compare); //時間順＋報酬

            // 後ろから順に大きいものを選ぶ?
            // もらえる時間順に並べ　さらに報酬順に並べる　それでhashを使ってその報酬の位置を得て　このときhashは使うたびに+1
            var ans = 0L;
            var pq = new PriorityQueue<int>(N, (a, b) => b - a);
            var index = 0;
            var count = 0;

            for (int i = M - 1; i >= 0; i--) // day
            {
                while (list[index][0] == M - i)
                {
                    pq.Enqueue(list[index][1]);
                    index++;
                    count++;
                }

                if (count > 0)
                {
                    ans += pq.Dequeue();
                    count--;
                }
            }

            Console.WriteLine(ans);
        }

        static int Compare(int[] a, int[] b)
        {
            var s = a[0] - b[0];
            return s == 0 ? b[1] - a[1] : s;
        }
    }

    // 優先度付き待ち行列（ヒープ）
    public class PriorityQueue<T>
    {
        private readonly List<T> m_list;
        private readonly Func<T, T, int> m_compare;
        private int m_count;

        public PriorityQueue(int capacity, Func<T, T, int> compare)
        {
            m_list = new List<T>(capacity);
            m_compare = compare;
            m_count = 0;
        }

        private int Add(T value)
        {
            if (m_count == m_list.Count)
            {
                m_list.Add(value);
            }
            else
            {
                m_list[m_count] = value;
            }
            return m_count++;
        }

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

        public void Enqueue(T value)
        {
            int c = Add(value);
            while (c > 0)
            {
                int p = (c - 1) / 2;
                if (m_compare(m_list[c], m_list[p]) < 0) { Swap(p, c); } else { break; }
                c = p;
            }
        }

        public T Dequeue()
        {
            T value = m_list[0];
            m_list[0] = m_list[--m_count];
            int p = 0;
            while (true)
            {
                int c1 = p * 2 + 1;
                int c2 = p * 2 + 2;
                if (c1 >= m_count) { break; }
                int c = (c2 >= m_count || m_compare(m_list[c1], m_list[c2]) < 0) ? c1 : c2;
                if (m_compare(m_list[c], m_list[p]) < 0) { Swap(p, c); } else { break; }
                p = c;
            }
            return value;
        }
    }
}