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
// $n = (int)trim(fgets(STDIN));
$input = explode(' ', trim(fgets(STDIN)));

$n = (int)$input[0];
$m = (int)$input[1];

$tasks = [];
for ($i=0; $i < $n; $i++) { 
	$input = explode(' ', trim(fgets(STDIN)));
	$a = (int)$input[0];
	$b = (int)$input[1];
	if ($a > $m) {
		continue;
	}
	$tasks[] = [$a, $b];
}
usort($tasks, function($x, $y){
	return $x[0] - $y[0];
});
$pq = new PriorityQueue();

$t_idx = 0;
$sum = 0;
for ($i=0; $i < $m; $i++) { 
	$rem_day = $i+1;
	while (isset($tasks[$t_idx]) && $tasks[$t_idx][0] <= $rem_day) {
		$pq->insert($tasks[$t_idx][1]);
		++$t_idx;
	}
	$max = $pq->extract();
	if ($max !== NULL) {
		$sum += $max;
	}
}

echo $sum;

/**
 * 
 */
class PriorityQueue
{
	private $data = [];

	public function insert($d){
		$h = count($this->data);
		$this->increaseKey($h+1, $d);
	}

	private function increaseKey($idx, $d){
		$this->data[$idx] = $d;
		$parent = (int)floor($idx/2);
		while ($idx > 1 && $this->data[$parent] < $this->data[$idx]) {
			$tmp = $this->data[$idx];
			$this->data[$idx] = $this->data[$parent];
			$this->data[$parent] = $tmp;
			$idx = $parent;
			$parent = (int)floor($idx/2);
		}
	}

	public function extract(){
		$result = null;
		$h = count($this->data);
		if ($h > 0) {
			$result = $this->data[1];
			$this->data[1] = $this->data[$h];
			unset($this->data[$h]);
			if ($h !== 1) {
				$this->data = $this->maxHeapify($this->data, 1);
			}
		}
		return $result;
	}

	private function maxHeapify($array, $i){
		$h = count($array);
		$l_idx = 2 * $i;
		$r_idx = (2 * $i) + 1;
		$largest = $i;
		if ($l_idx <= $h && $array[$l_idx] > $array[$i]) {
			$largest = $l_idx;
		}
		if ($r_idx <= $h && $array[$r_idx] > $array[$largest]) {
			$largest = $r_idx;
		}

		if ($largest !== $i) {
			$tmp = $array[$largest];
			$array[$largest] = $array[$i];
			$array[$i] = $tmp;
			$array = $this->maxHeapify($array, $largest);
		}
		return $array;
	}

}