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: Accepted)

#include<bits/stdc++.h>
using namespace std;
const int N = 2e5+5;
typedef long long ll;
const int num = 1e3 + 5;

int n,d,a;
ll ans;

struct point{
  int place = 0,health = 0,diff;
}li[N];

int main(){
  // freopen("input.txt","r",stdin);
  ios::sync_with_stdio(false);
  cin>>n>>d>>a;
  for(int i = 1;i <= n;i++){
    cin>>li[i].place>>li[i].health;
  }
  sort(li+1,li+n+1,[](point x,point y){return x.place < y.place;});
  for(int i = 1;i < n;i++) li[i].diff = li[i+1].health - li[i].health;
  d <<= 1;
  int l = 1,r = 1,cur = li[1].health;
  while(l <= n){
    while(r <= n && li[r+1].place - li[l].place <= d) {r++;}
    int tmp = (cur/a + (cur % a != 0));
    ans += tmp;
    cur -= tmp*a;
    li[r].diff += tmp*a;
    while(cur <= 0){
      cur += li[l++].diff;
    }
  }
  cout<<ans<<endl;
  return 0;
}