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<bits/stdc++.h>
typedef long long ll;
typedef long double ld;
#define FASTIO ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define PRECISION std::cout << std::fixed << std::setprecision(20);
  
using namespace std;
 
const ll inf = 1e18;
const ll N = 1e5;
const ll bits = 62;
const ll mod = 1e9+7;
const ld pi = 3.14159265358979323846;

struct mons{
    ll h,x;

    bool operator < (mons other) const {
        return x < other.x;
    }
};

struct coord{
    ll x;
    ll a;

    bool operator < (coord other) const {
        return x < other.x;
    }
};


int main(){
    FASTIO;
    PRECISION;

    ll n,d,a;
    cin>>n>>d>>a;

    vector<mons>arr(n);

    for(int i=0;i<n;i++){
        cin>>arr[i].x>>arr[i].h;
    }

    sort(arr.begin(),arr.end());

    ll cx=-1,b=0;
    priority_queue<coord>pq1,pq2;
    coord temp;

    ll ans = 0;


    for(int i=0;i<n;i++){
        // now remove non overlapping
        while(!pq2.empty() && pq2.top().x<arr[i].x){
            temp = pq2.top();
            b-=temp.a;
            pq2.pop();
        }

        // take all that you can take
        while(!pq1.empty() && pq1.top().x>=arr[i].x){
            temp = pq1.top();
            b+=temp.a;
            pq2.push(temp);
            pq1.pop();
        }
        // cout<<b<<"\n";
        arr[i].h-=b;
        // drop more bombs
        if(arr[i].h>0){
            ll req = arr[i].h / a;
            if(req*a<arr[i].h) req++;
            ans+=req;
            temp.a = req*a;
            b+=temp.a;
            temp.x = arr[i].x + 2LL*d;
            pq2.push(temp);
        }
        
        // now remove non overlapping
        while(!pq2.empty() && pq2.top().x<=arr[i].x){
            temp = pq2.top();
            b-=temp.a;
            pq2.pop();
        }

    }

    cout<<ans<<"\n";

}