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 Int = long long;
int main() {
    int N, M; cin >> N >> M;
    vector<pair<int, int>> V(N);
    for (int i = 0; i < N; i++) {
        int A, B; cin >> A >> B;
        V[i] = make_pair(B, A);
    }
    sort(rbegin(V), rend(V));
    set<int> S;
    for (int i = 0; i < M; i++) S.insert(end(S), i);
    Int ans = 0;
    for (int i = 0; i < N; i++) {
        int b, a; tie(b, a) = V[i];
        auto it = S.upper_bound(M - a);
        if (it != begin(S)) {
            S.erase(prev(it));
            ans += b;
        }
    }
    cout << ans << endl;
    return 0;
}