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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

long long INF=pow(10LL, 16LL);

int main(){
  long N, D, A;
  cin >> N >> D >> A;
  
  pair<long, long> monsters[N]; //place, hp
  for (int i = 0; i < N; i++) {
    long X, H;
    cin >> X >> H;
    monsters[i]={X,H};
  }
  sort(monsters, monsters+N);
  
  //start
  int startIdx = 0;
  long ans = 0;
  while (!(startIdx==N-1&&monsters[startIdx].second<=0)) {
    long x = monsters[startIdx].first + D;
    long atacks = (monsters[startIdx].second + A - 1L) / A;
    ans += atacks;
    
    int i = startIdx;
    //atack.
    while(monsters[i].first <= x+D){
      long killAtacks = (monsters[i].second + A - 1L) / A;
      if (killAtacks < atacks) {
        monsters[i].second = 0;
      } else {
	    monsters[i].second -= A*atacks;
      }
      i++;
    }
    //change index.
    i = startIdx;
    while(monsters[i].second <= 0 && monsters[i].first <= x+D){
      i++;
    }
    startIdx = min(i,(int)N-1);
  }
  
  cout << ans << endl;
  
  return 0;
}