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 <queue>

using namespace std;

int main()
{
	int N, M;
	cin >> N >> M;
	
	vector<vector<int>> jobs(M);
	
	for (int i = 0; i < N; i++)
	{
		int A, B;
		cin >> A >> B;
		
		// M日より大きいA日の仕事は報酬をもらえないため、報酬の仕事として扱わない。
		if (A > M)
		{
			continue;
		}
		
		// 報酬BをもらうにはM - A日までに仕事を行う必要があるため
		jobs[M - A].push_back(B);
	}
	
	// 常に最大の値を取り出すためにpriority_queueを利用
	priority_queue<int> q;
	
	long answer = 0;
	// 最終日 - 1から処理を行う 貪欲法
	for (int i = M - 1; i >= 0; i--)
	{
		// キューにjobs[i]に格納された全ての報酬Bを入れる
		for (int b: jobs[i])
		{
			q.push(b);
		}
		
		if (!q.empty())
		{
			// 格納されたqの先頭の要素がjobs[i]の一番高い報酬になる
			answer += q.top();
			// 先頭のtop()を削除する
			q.pop();
		}
	}
	
	cout << answer << endl;
	
	return 0;
}