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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
  const DAY = 0;
  const MONEY = 1;
  const FLAG = 2;
  
  $tmp = explode(" ", trim(fgets(STDIN)));
  $n = $tmp[0];
  $m = $tmp[1];

  $data = [];
  $arrayMoney = [];
  $arrayDay = [];
  for($i=0; $i<$n; $i++){
    $tmp = explode(" ", trim(fgets(STDIN)));
    
    //日数がMを超えていれば考慮外
    if($tmp[DAY]<=$m){
      $arrayDay[] = $tmp[DAY];
      $arrayMoney[] = $tmp[MONEY];

      $tmp[2] = false;
      $data[] = $tmp;
    }
  }

  array_multisort($arrayMoney, SORT_DESC, $arrayDay, SORT_DESC, $data);

  $total = 0;
  $minIdx = 0;
  for($i=0; $i<$m; $i++){
    $newMin = -1;
    for($j=$minIdx; $j<$n; $j++){
      if($data[$j][FLAG]==false){
        
        if($newMin==-1){
          $newMin = $j;
        }
        if($i+$data[$j][DAY]<=$m){
          $data[$j][FLAG] = true;
          $total += $data[$j][MONEY];
          break;
        }
        
      }else{
        //実施済みなら次へ
      }
    }
    
    $miIdx = $newMin;
  }

  echo $total."\n";