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: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

struct Monster {
	ll x;
	ll health;

	bool operator<(const Monster other) {
		return this->x < other.x;
	}
};

ll n, d, dmg;
vector<Monster> v;
vector<ll> bombs;

int main() {
	ios::sync_with_stdio(false);
	cin >> n >> d >> dmg;
	v.resize(n);
	bombs.resize(n, 0);
	for (Monster& monster : v) cin >> monster.x >> monster.health;
	sort(begin(v), end(v));
	ll ans = 0;
	ll acc = 0;
	for (int i = 0; i < n; i++) {
		acc += bombs[i];
		v[i].health -= acc * dmg;
		if (v[i].health > 0) {
			ll rem = (v[i].health + dmg - 1) / dmg;
			ll b = 0, e = n, target = v[i].x + 2 * d;
			while (b < e) {
				ll mid = (b + e) / 2;
				if (v[mid].x > target) {
					e = mid;
				} else {
					b = mid + 1;
				}
			}
			if (b < n) bombs[b] -= rem;
			acc += rem;
			ans += rem;
		}
	}
	cout << ans << endl;
	return 0;
}