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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <queue>

#define debug(x) std::cout << #x << " = " << (x) << std::endl;

using namespace std;
using ll = long long;
using pll = pair<ll, ll>;

int main()
{
    ll num, dist, dmg;
    cin >> num >> dist >> dmg;

    priority_queue< pll, vector<pll>, greater<pll> > min_heap;

    for(ll i=0; i<num; i++)
    {
        ll pos, life;
        cin >> pos >> life;

        min_heap.push({pos, life});
    }

    ll total_hits  = 0;
    ll acc_dmg = 0;
    queue<pll> log;

    while(!min_heap.empty())
    {
        auto [pos, life] = min_heap.top();
        min_heap.pop();

        while(log.size())
        {
            auto [dmg_area, qtd_bombs] = log.front();

            // this bomb did not hit this region
            if(dmg_area <  pos) {
                log.pop();
                acc_dmg -= dmg * qtd_bombs;
            }

            else break;
        }

        // rightmost position that hits the target
        ll dmg_limit_area = pos + dist + dist;

        // subtracting dmg from bombs exploded in the region
        life -= acc_dmg;
        if(life <= 0) continue;

        // ceil division (without overflow)
        ll hits_need = 1 + ((life - 1)/dmg);

        total_hits += hits_need;

        // Accumulated dmg from previous bombs that exploded in this region
        acc_dmg += dmg * hits_need;


        // remeber how many bombs exploded at this region
        log.push({dmg_limit_area, hits_need});
    }

    cout << total_hits << '\n';

    return 0;
}