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;

using lint = long long;

int main(){
    long N, M;
    long A, B;
    pair<long, long> AB[100002];
    multiset<long> candidate;

    cin >> N >> M;
    for(long n=0;n<N;n++){
        cin >> A >> B;
        AB[n].first = A;
        AB[n].second = B;
    }
    sort(AB, AB+N);
    long ABindex = 0;
    long long ans = 0;
    for(long mbefore=1;mbefore<=M;mbefore++){
        while(AB[ABindex].first <= mbefore && ABindex < N){
            candidate.insert(AB[ABindex].second);
            ABindex++;
        }
        if(candidate.size() > 0){
            auto itr = candidate.end();
            itr--;
            ans += *itr;
            candidate.erase(itr);
        }
    }
    cout << ans << endl;
    return 0;
}