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.*
import java.io.PrintWriter

val pw = PrintWriter(System.out)
val MOD = 1000000007L
val INF = 2147483647
val LINF = 9223372036854775807L

fun main(args: Array<String>){
    solve()
    pw.flush()    
}

fun solve(){
    val (n, d, a) = nextIntList()
    val ary = Array(n) { LongArray(2) { 0 } }
    repeat(n) { 
        val (x, h) = nextLongList()
        ary[it][0] = x
        ary[it][1] = h
    }
    val mons = ary.sortedBy { it[0] }   // X基準でソート

    val bomb = IntArray(n)  // モンスターiを左端としたとき、右端となるモンスター
    for (i in mons.indices) {
        val border = mons[i][0] + 2 * d
        var ok = -1
        var ng = mons.size
        while(abs(ok - ng) > 1){
            val mid = (ok + ng) / 2
            if(mons[mid][0] <= border){
                ok = mid
            } else {
                ng = mid
            }
        }
        bomb[i] = ok
    }

    var ans = 0L
    val damage = LongArray(n + 1)   // 爆風のダメージ imos法による累積和
    for (i in mons.indices) {
        if(i >= 1){
            damage[i] += damage[i - 1]
        }
        if(mons[i][1] - damage[i] <= 0) continue    // 既にHが0になっているなら無視
        val count = ((mons[i][1] - damage[i]) + (a - 1)) / a
        ans += count
        damage[i] += count * a
        damage[bomb[i] + 1] -= count * a
    }

    println(ans)

}

// Print
fun println(v: String){
    pw.println(v)
}
fun print(v: String){
    pw.print(v)
}

// Read
fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ")
fun nextIntList() = next().split(" ").map{ it.toInt() }
fun nextLongList() = next().split(" ").map{ it.toLong() }
fun nextDoubleList() = next().split(" ").map{ it.toDouble() }
fun nextAryln(n: Int) = Array(n){ next() }
fun nextIntAryln(n: Int) = IntArray(n){ nextInt() }
fun nextLongAryln(n: Int) = LongArray(n){ nextLong() }
fun nextDoubleAryln(n: Int) = DoubleArray(n) { nextDouble() }

// Math
fun abs(n: Int) : Int = Math.abs(n)
fun abs(n: Long) : Long = Math.abs(n)
fun abs(n: Double) : Double = Math.abs(n)
fun max(a: Long = -LINF, b: Long = -LINF, c: Long = -LINF, d: Long = -LINF, e: Long = -LINF): Long = listOf(a, b, c, d, e).max()!!.toLong()
fun min(a: Long = LINF, b: Long = LINF, c: Long = LINF, d: Long = LINF, e: Long = LINF): Long = listOf(a, b, c, d, e).min()!!.toLong()
fun prime(from: Long, to: Long = from) : List<Long>{
    return (from..to).filter{ i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all{ j -> i % j != 0L}
    }
}
fun gcd(a: Long, b: Long) : Long = if(a % b == 0L) b else gcd(b, (a % b))
fun lcm(a: Long, b: Long) : Long = a / gcd(a, b) * b
fun modpow(a: Long, n: Long, p:Long = MOD) : Long {
    var res = 1L
    var ar = a
    var nr = n
    while(nr > 0){
        if((nr and 1) == 1L) res = res * ar % p
        ar = ar * ar % p
        nr = nr shr 1
    }
    return res
}
fun modinv(a: Long, p: Long = MOD) : Long = modpow(a, p - 2, p)
fun ncr(n: Long, r: Long) : Long {
    var a = 1L
    var b = 1L
    for (i in 1..r) {
        a = a * (n + 1 - i) % MOD
        b = b * i % MOD
    }
    return modinv(b, MOD) * a % MOD
}