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)

fun main(args: Array<String>) {
    abc153f()
}

fun abc153f() {
    val (n, length, damage) = readLine()!!.split(' ').map { it.toInt() }
    val xhList = (1..n).map {
        readLine()!!.split(' ').map { it.toInt() }.let { Pair(it[0], it[1]) }
    }
        .sortedBy { it.first }

    val positions = IntArray(n)
    val hps = IntArray(n)
    xhList.mapIndexed { index, pair ->
        positions[index] = pair.first
        hps[index] = pair.second
    }

    var answer = 0L
    for (i in 0 until n) {
        val pos = positions[i]
        val hp = hps[i]
        if (hp <= 0) continue

        val need = Math.ceil(hp.toDouble() / damage).toInt()
        answer += need

        val lowerBound = lowerBound(positions, pos + length * 2)
        (i..Math.min(lowerBound, n - 1)).map { hps[it] -= need * damage }
    }

    println(answer)
}

private fun lowerBound(list: IntArray, key: Int): Int {
    var ng = -1
    var ok = list.size

    while (ok - ng > 1) {
        val mid = (ok + ng) / 2
        if (list[mid] >= key) ok = mid else ng = mid
    }
    return ok
}