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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <climits>
#include <cstdlib>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <vector>
#define DEBUG 1
using namespace std;
constexpr int kMod = 1000000007;
typedef long long LL;
typedef pair<LL, LL> P;

int main() {
  LL N, D, A; cin >> N >> D >> A;
  vector<P> X(N);
  vector<LL> carry(N + 1, 0);
  for (int i = 0; i < N; ++i) {
    int x; double h; cin >> x >> h;
    int atk = ceil(h/A);
    X[i] = {x, atk};
  }

  LL total_atk = 0;
  LL damage = 0;
  sort(X.begin(), X.end());
  for (int i = 0; i < N; ++i) {
    damage -= carry[i];
    if (X[i].second <= damage) continue;
    X[i].second -= damage;

    total_atk += X[i].second;
    damage += X[i].second;
    LL last = X[i].first + 2 * D + 1;
    LL j = i + 1;
    while(X[j].first <= last && j < N) {
      ++j;
    }
    carry[j] += X[i].second;
  }
  cout << total_atk << endl;
}