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>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define printYes() cout << "Yes" << endl;
#define printNo() cout << "No" << endl;
#define printVector(v) rep(i, v.size()) cout << x << endl;

int main()
{
    int N, D, A;
    cin >> N >> D >> A;
    D = 2 * D + 1;
    vector<pair<long long, long long>> monster(N);
    vector<long long> kill_bomb(N);
    rep(i, N)
    {
        int X, H;
        cin >> X >> H;
        monster[i] = make_pair(X, H);
    }
    sort(monster.begin(), monster.end());

    long long ans = 0;
    long long count = monster[0].second / A;
    if (monster[0].second % A != 0)
        count++;
    kill_bomb[0] = count;
    ans += count;
    rep(i, N - 1)
    {
        long long HP = monster[i + 1].second;
        if (monster[i + 1].first <= monster[i].first + D)
        {
            HP -= A * kill_bomb[i];
            kill_bomb[i + 1] = kill_bomb[i];
        }
        if (HP <= 0)
            continue;
        long long count = HP / A;
        if (HP % A != 0)
            count++;
        kill_bomb[i + 1] += count;
        ans += count;
    }
    cout << ans << endl;
    return 0;
}