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: Time Limit Exceeded)

import java.io.*
import java.util.*
import kotlin.comparisons.compareByDescending

fun solve(N: Int, M: Int, A: IntArray, B: IntArray){
    data class Job(val salary: Int, val time: Int)
    val jobs = (0 until N)
        .map{ Job(B[it], A[it]) }
        .sortedBy{ it.time }
    var ans = 0
    val queue = PriorityQueue<Int>(1, compareByDescending { it })
    var left = 0
    for (day in M-1 downTo 0){
        val onTimeIdx = jobs.map{ it.time }.upperBound(M - day)
        jobs.drop(left).take(onTimeIdx - left).map{ queue.offer(it.salary) }
        ans += queue.poll()?: 0
        left = onTimeIdx
    }
    println(ans)
    return
}

fun <T : Comparable<T>> List<T?>.upperBound(
        element: T,
        fromIndex: Int = 0,
        toIndex: Int = size
): Int {
    var low = fromIndex
    var high = toIndex
    while (low < high) {
        val mid = (low + high) / 2
        if (element >= this.get(mid)!!) {
            low = mid + 1
        } else {
            high = mid
        }
    }
    return low
}

fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val N = sc.next().toInt()
    val M = sc.next().toInt()
    val A = IntArray(N)
    val B = IntArray(N)
    for (i in 0 until N) {
        A[i] = sc.next().toInt()
        B[i] = sc.next().toInt()
    }
    solve(N, M, A, B)
}