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 C (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
int N, D, A;
typedef struct {int x; int h;} Fox;
Fox fox[200200];

int c(const void *a, const void *b) {
  return ((Fox *)a)->x - ((Fox *)b)->x;
}

int main() {
  int i, j;
  long long total_count = 0;
  scanf("%d %d %d", &N, &D, &A);
  for (i = 0; i < N; i++) {
    int x, h;
    scanf("%d %d", &x, &h); fox[i].x = x; fox[i].h = h;
  }
  qsort(fox, N, sizeof(Fox), c); // 昇順ソート                                  
  for (i = 0; i < N; i++) {
    if (fox[i].h <= 0) continue;
    int bomb_count = ((fox[i].h + A - 1) / A);
    int damage = bomb_count * A;
    int x2 = fox[i].x + D * 2;
    for (j = i; j < N; j++) {
      if (fox[j].x > x2) break;
      fox[j].h -= damage;
    }
    total_count += bomb_count;
  }
  printf("%lld\n", total_count);
}