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 PHP (5.6.30) (judge verdict: Accepted)

<?php

$str = trim(fgets(STDIN));
list ($n, $m) = array_map("intval", explode(" ", $str));

$array = [];
for ($i=0; $i<$n; $i++) {
    $tmpStr = trim(fgets(STDIN));
    list ($day, $reward) = array_map("intval", explode(" ", $tmpStr));
    // 報酬が多い順、日数が少ない順にsortして、順番に受けていく
    // 残り日数的に受けられない仕事はスキップ

    if ( !isset($array[$day]) ) {
        $array[$day] = [];
    }
    $array[$day][] = $reward;
}

ksort($array);


$result = 0;
$queue = new SplPriorityQueue();
for ($i=$m-1; 0<=$i; $i--) {
    $remain = $m-$i;

    if ( isset($array[$remain]) ) {
        foreach ($array[$remain] as $reward) {
            $queue->insert($reward, $reward);
        }
    }

    if (!$queue->isEmpty()) {
        $result += $queue->extract();
    }
}

echo "$result\n";