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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) = yorukatsu19e()

fun yorukatsu19e() {
    val (n, width, damage) = readLine()!!.split(' ').map { it.toLong() }
    data class Monster(val position: Long, val health: Long)

    val monsters = (1..n).map {
        readLine()!!.split(' ').map { it.toLong() }.let { Monster(it[0], it[1]) }
    }.sortedBy { it.position }

    data class Bomb(val end: Long, val amount: Long)

    val bombs = ArrayDeque<Bomb>()
    var currDamageSum = 0L
    var answer = 0L

    for ((position, health) in monsters) {
        while (bombs.isNotEmpty() && bombs.peek().end < position) {
            val bomb = bombs.poll()
            currDamageSum -= damage * bomb.amount
        }
        val need = Math.max(Math.ceil((health - currDamageSum).toDouble() / damage).toLong(), 0)
        if (need == 0L) continue
        currDamageSum += need * damage
        bombs.add(Bomb(position + width * 2, need))
        answer += need
    }

    println(answer)
}