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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main(){
    int n, m;
    cin >> n >> m;
    pair <int, int> works[n];
    for (int tsumugi = 0; tsumugi < n; tsumugi++){
        cin >> works[tsumugi].first >> works[tsumugi].second;
    }

    sort(works, works + n);

    //最終日の前日から考察する
    int reward = 0;
    priority_queue <int> queue;
    int index = 0;
    for (int remainDays = 1; remainDays <= m; remainDays++){
        while (works[index].first == remainDays){
            queue.push(works[index].second);
            index++;
        }
        if(!queue.empty()){
            reward += queue.top();
            // cout << "remain days:" << remainDays << endl;
            // cout << "top:" << queue.top() << endl;
            // cout << "size:" << queue.size() << endl;
            queue.pop();
            // cout << "poped size:" << queue.size() << endl;
        }
    }    

    cout << reward << endl;
    return 0;
}