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 <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <cmath>
#include <iomanip>
#include <queue>
#include <climits> 

struct AB
{
    long A;
    long B;
    AB(long A1, long B1)
    {
        A=A1;
        B=B1;
    }
    bool operator <(const AB &another) const
    {
        return A<another.A;
    };
};

int main()
{
    long N,M;
    std::cin >> N >> M;
    std::vector<AB> ABs;
    for(long i=0; i<N; i++){
        long A,B;
        std::cin >> A >> B;
        ABs.push_back(AB(A,B));
    }
    std::sort(ABs.begin(),ABs.end());

    std::priority_queue<long> queue;
    long result=0;
    long depth=0;
    for(long i=1; i<=M; i++){
        while(ABs[depth].A<=i && depth<N){
            queue.push(ABs[depth].B);
            depth++;
        }
        if(queue.size()>0){
            result+=queue.top();
            queue.pop();
        }
    }
    std::cout << result << std::endl;
    return 0;
}