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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func scanInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return i
}

type task struct {
	day, price int
}

type theap []task

func (h theap) Len() int           { return len(h) }
func (h theap) Less(i, j int) bool { return h[i].price > h[j].price } // maxにするためにあえて変更
func (h theap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }

func (h *theap) Push(x interface{}) {
	*h = append(*h, x.(task))
}

func (h *theap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]

	return x
}

func main() {
	sc.Split(bufio.ScanWords)
	N, M := scanInt(), scanInt()

	jobs := make(map[int][]int)
	for i := 0; i < N; i++ {
		A, B := scanInt(), scanInt()
		jobs[A] = append(jobs[A], B)
	}

	ans := 0
	H := make(theap, N)
	heap.Init(&H)
	for day := 1; day <= M; day++ {
		for _, t := range jobs[day] {
			heap.Push(&H, task{day, t})
		}
		if H.Len() > 0 {
			selected := heap.Pop(&H).(task)
			ans += selected.price
		}
	}
	fmt.Println(ans)
}