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<iostream>
#include<algorithm>
#include<vector>
using namespace std;
using ll = long long;
constexpr ll linf=2*1e18;

int main(){
    ll n,d,a;
    cin>>n>>d>>a;
    vector<pair<ll,ll>> p(n);
    for(int i=0;i<n;i++){
        ll x,h;
        cin>>x>>h;
        p[i]=make_pair(x,h);
    }
    sort(p.begin(),p.end());
    vector<ll> x(n);
    vector<ll> h(n);
    for(int i=0;i<n;i++){
        x[i]=p[i].first;
        h[i]=(p[i].second+a-1)/a;
    }
    vector<ll> e(n);
    for(int i=0;i<n;i++){
        e[i] = (lower_bound(x.begin(),x.end(),x[i]+2*d)- x.begin());
    }
    vector<ll> damage(n+2,0);
    ll ans=0;
    for(int i=0;i<n;i++){
        if(i==0){
            damage[i]=h[i];
            ans+=h[i];
            damage[e[i]+1]-=damage[i];
        }
        else{
            damage[i]+=damage[i-1];
            if(damage[i]>h[i]){
                continue;
            }
            else{
                ll res=h[i]-damage[i];
                damage[i]+=res;
                ans+=res;
                damage[e[i]+1]-=res;
            }
        }
    }
    /*for(int i=0;i<n;i++){
        cout<<damage[i]<<endl;
    }*/
    cout<<ans<<endl;
    return 0;
}