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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int D = sc.nextInt();
        int A = sc.nextInt();

        PriorityQueue<Pair> pq = new PriorityQueue<>((a,b)->a.x-b.x);
        for (int i = 0; i < N; i++) {
            int x = sc.nextInt();
            int h = sc.nextInt();
            pq.offer(new Pair(x, h));
        }

        long totalDamage = 0;
        long ans = 0;
        LinkedList<Pair> q = new LinkedList<>();
        while (!pq.isEmpty()) {
            Pair m = pq.poll();
            int x = m.x;
            long h = m.v;
            while (q.size() > 0 && q.peek().x < x) {
                totalDamage -= q.poll().v;
            }
            
            if (h >= totalDamage) {
                h -= totalDamage;
                long atackNum = Math.max((h+A-1)/A, 0);
                ans += atackNum;
                totalDamage += atackNum*A;
                q.offer(new Pair(x+2*D, atackNum*A));
            }
        }

        System.out.println(ans);
    }

    private static class Pair {
        private final int x;
        private final long v;
        Pair(int x, long v) {
            this.x = x;
            this.v = v;
        }
    }
}