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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.*
import java.math.*
import java.lang.*
import kotlin.comparisons.*

val pw = PrintWriter(System.out)
val MOD: Long = (1e+9 + 7).toLong()

data class Job(val a: Int, val b: Int)

fun main(args: Array<String>) {
    val (n, m) = readListOfInt()    

    val jobs = (0 until n).map { 
        val (a, b) = readListOfInt()
        Job(a, b)
    }.sortedBy { it.a }

    var ans = 0L
    var jobIdx = 0
    val que = PriorityQueue<Int>(1, compareByDescending { it })
    for(day in 1..m) {
        while(jobIdx < n && jobs[jobIdx].a <= day) {
            que.add(jobs[jobIdx].b)
            jobIdx++
        }
        ans += que.poll()?: 0
    }

    println(ans)

    pw.flush()
}

/****** Declared Functions and Data Structures ******/
// IO
fun read() = readLine()!!
fun readInt() = read().toInt()
fun readLong() = read().toLong()
fun readDouble() = read().toDouble()
fun readListOfString() = read().split(" ")
fun readListOfInt() = readListOfString().map { it.toInt() }
fun readListOfLong() = readListOfString().map { it.toLong() }
fun readListOfDouble() = readListOfString().map { it.toDouble() }

fun Double.format(digits: Int) = String.format("%.${digits}f", this)
fun Float.format(digits: Int) = String.format("%.${digits}f", this)

fun print(value: Any) { pw.print(value) }
fun println(value : Any) { pw.println(value) }

fun<T> permutations(src: List<T>): List<List<T>> {
    if(src.size == 1) return listOf(src)
    val perms = mutableListOf<List<T>>()
    val insertElement = src[0]
    permutations(src.drop(1)).forEach { perm ->
        for(i in 0..perm.size) {
            val newPerm = perm.toMutableList()
            newPerm.add(i, insertElement)
            perms.add(newPerm.toList())
        }
    }
    return perms
}

// return nCr, if you want nCr, please access v[n][r]
fun combinations(n: Long): List<List<Long>> {
    val v = (0..n).map { (0..n).map{0L}.toMutableList() }.toMutableList()
    for(i in 0 until v.size) {
        v[i][0] = 1L
        v[i][i] = 1L
    }
    for(i in 0 until v.size) {
        for(j in 1 until i) {
            v[i][j] = (v[i-1][j-1] + v[i-1][j]) % MOD
        }
    }
    return v.map { it.toList() }.toList()
}

// should be a >= b
fun gcd(a: Long, b: Long): Long = 
    if(b == 0L) a else gcd(b, a % b)

// shoud be a >= b
fun lcm(a: Long, b: Long): Long = 
    a / gcd(a, b) * b

fun sumDigits(num_: Long): Long {
    var num = num_
    var rtn: Long = 0
    while(num != 0.toLong()) {
        val tmp = num % 10
        rtn += tmp
        num /= 10
    }
    return rtn
}

fun isDecimal(v: Double): Boolean = ((v - Math.floor(v)) != 0.0)

// Data Structures
class Stack<T>(private var st: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = st.isEmpty()
    fun top(): T = st.last()
    fun push(e: T) { st.add(e) }
    fun pop() { st = st.dropLast(1).toMutableList() }
}

class Queue<T>(private var que: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = que.isEmpty()
    fun top(): T = que.first()
    fun push(e: T) { que.add(e) }
    fun pop() { que = que.drop(1).toMutableList() }
}