Problem:
Score : 600 points

Problem Statement

Silver Fox is fighting with N monsters.

The monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.

Silver Fox can use bombs to attack the monsters.
Using a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.
There is no way other than bombs to decrease the monster's health.

Silver Fox wins when all the monsters' healths become 0 or below.

Find the minimum number of bombs needed to win.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq D \leq 10^9

1 \leq A \leq 10^9

0 \leq X_i \leq 10^9

1 \leq H_i \leq 10^9

X_i are distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N D A
X_1 H_1
:
X_N H_N

Output

Print the minimum number of bombs needed to win.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.

Solution in Scala (2.11.7) (judge verdict: Accepted)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Stack, Queue, PriorityQueue, Set}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N, D, A = in.next().toInt
  var hoge = new Array[(Long, Int)](N)
  for (i <- 0 until N) {
    val X, H = in.next().toInt
    hoge(i) = (X, H)
  }

  hoge = hoge.sorted

  // 
  val c = new Array[(Long, Int)](N+2) // (x, HP)
  c(N+1) = (Long.MaxValue, 0)
  for (i <- 1 to N) {
    c(i) = hoge(i-1)
  }

  def check(i: Int, n: Long): Boolean = {
    val (ind, _) = c(i)
    n < ind
  }

  // 条件を満たす最小の値を返す
  def binarySearch(min: Int, max: Int, n: Long): Int = {
    val mid: Int = (max + min) / 2
      (max - min) match{
      case 0 | 1 =>
        check(min, n) match{
          case true  => min
          case false => max
        }
      case _ =>
        (check(mid, n)) match{
          case true  => binarySearch(min, mid, n)
          case false => binarySearch(mid, max, n)
        }
    }
  }

  val memo = new Array[Long](N+2) // 適用爆弾数の調整値
  var hand = 0L
  var ans = 0L
  for (i <- 1 to N) {
    val (x, hp) = c(i)
    hand -= memo(i)

    if (hand * A < hp) {
      val fuga = hp - hand * A
      val num = (fuga + (A-1)) / A // 必要投下爆弾数

      ans += num
      hand += num
      // にぶたん使って - をメモる
      val ind = binarySearch(i+1, N+1, x.toLong + 2L*D)
      memo(ind) += num
    }
  }

  println(ans)
}

object Sub {
  def print2DimArray[A](mat: Array[Array[A]]): Unit = {
    mat.foreach(lin => println(lin.deep))
  }
}

class InputReader(stream: InputStream) {
  private[this] val reader = new BufferedReader(new InputStreamReader(stream))
  private[this] var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}