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: Wrong Answer)

data class Pa(val x: Long, var h: Long)
fun main(args: Array<String>) {
    val (N, D, A) = listOfInt()
    val XH = Array<Pa>(N) {
        var (x, h)= listOfLong()
        Pa(x, h)
    }.sortedBy { it.x }.toMutableList()
    val DD = 2 * D
    val D2 = Array<Int>(N) { 0 }
    var left = 0
    var right = 0
    while (left < N) {
        if (XH[left].x + DD >= XH[right].x) {
            D2[left] = right
            right += 1
            if (right >= N) {
                left += 1
                right = left
            }
        }
        else left += 1
    }
    var ans = 0L
    var total = 0L
    XH.forEach { total += it.h }
    while (total > 0) {
        repeat(N) {
            if (XH[it].h > 0) {
                val count = (XH[it].h + A - 1) / A
                ans += count
                val dmage = count * A
                for (p in it..D2[it]) {
                    val md = Math.max(dmage, XH[p].h)
                    XH[p].h -= md
                    total -= md
                }
            }
        }
    }
    println(ans)
}
fun next() = readLine()!!
fun nextLong() = next().toLong()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfLong() = listOfString().map(String::toLong)