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 Python (3.4.3) (judge verdict: Runtime Error)

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

int main() {
long long ans = 0;
long long N,D,A;
cin >> N >> D >> A;
vector<vector<long long>> enemies(N, vector<long long> (2));
for (int i = 0; i < N; i++)
{
    cin >> enemies.at(i).at(0) >> enemies.at(i).at(1);
}
sort(enemies.begin(),enemies.end(),[](const vector<long long> &alpha,const vector<long long> &beta){return alpha[0] < beta[0];});

queue<vector<long long>> damage;
long long dmg = 0;
for (int i = 0; i < N; i++){
    long long x = enemies.at(i).at(0);
    long long h = enemies.at(i).at(1);
    if (damage.empty()){
        long long bomb = (h+A-1)/A;
        ans += bomb;
        dmg += bomb*A;
        damage.push({x+2*D,bomb});
    }
    else{
        while (!damage.empty()){
            vector<long long> vec;
            vec = damage.front();
            long long d = vec.at(0);
            long long bomb = vec.at(1);
            if (d < x){
                dmg -= bomb*A;
                damage.pop();
            }
            else{
                break;
            }
        }
        if (h > dmg){
            long long bomb = (h-dmg+A-1)/A;
            dmg += bomb*A;
            damage.push({x+2*D,bomb});
            ans += bomb;
        }
        
    }
}

cout << ans << endl;
}