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 PII = pair<int, int>;
#define F first
#define S second
int main() {
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<PII> v;
  for (int i = 0; i < n; ++i) {
    int a, b;
    cin >> a >> b;
    if (a <= m)
      v.emplace_back(m - a + 1, b);
  }
  sort(v.begin(), v.end());
  priority_queue<int, vector<int>, greater<int>> q;
  uint64_t ans = 0;
  for (auto &it : v) {
    int a, b;
    tie(a, b) = it;
    q.push(b);
    ans += b;
    while (q.size() > a) {
      ans -= q.top();
      q.pop();
    }
  }
  cout << ans << endl;
  return 0;
}