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.ArrayDeque

fun main(args: Array<String>) {
    val (N, D, A) = readInputLine().split(" ").map { it.toLong() }
    val mons = Array(N.toInt()) { val (X, H) = readInputLine().split(" ").map { it.toLong() }; Pair(X, H)}
    mons.sortBy { it.first }

    val damages = ArrayDeque<Pair<Long, Long>>()

    var ans = 0L
    var nowDamage = 0L

    for (m in mons) {
        while (damages.isNotEmpty()) {
            val (x, cnt) = damages.peek()!!
            if (x + D * 2 < m.first) {
                nowDamage -= cnt * A
                damages.poll()!!
            } else {
                break
            }
        }
        if (nowDamage >= m.second) {
            continue
        } else {
            val cnt = (m.second - nowDamage) / A + if ((m.second - nowDamage) % A != 0L) 1L else 0L
            damages.add(Pair(m.first, cnt))
            nowDamage += cnt * A
            ans += cnt
        }
    }

    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}