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: Time Limit Exceeded)

/*input
9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5
*/

//https://atcoder.jp/contests/abc153/tasks/abc153_f

#include <bits/stdc++.h>
#define ll long long
#define vi vector<int>

using namespace std;

void run() {
	int n, i, j;
	ll d, a;
	cin >> n >> d >> a;
	vector<pair<ll, ll>> monster(n);
	vector<int> prefix(n+1, 0);		// Prefix array to store how many bombs have already been dropped on future locations
	for(i=0; i<n; i++)
		cin >> monster[i].first >> monster[i].second;
	sort(monster.begin(), monster.end());
	i = 0;	// current monster
	ll ret = 0;
	while(i < n) {
		ll x = monster[i].first, h = monster[i].second;
		ll bomb_x = x + d;
		ll bombs = max(0ll, (h - prefix[i]*a + a - 1) / a);
		for(j=i; j<n; j++) {	// Monsters in range
			if(abs(monster[j].first - bomb_x) > d)
				break;
		}
		ret += bombs;
		prefix[i] += bombs;
		prefix[j] -= bombs;
		prefix[i+1] += prefix[i];
		i++;
	}
	cout << ret << endl;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);		
	int t = 1;
	// cin >> t;
	while(t--) {
		run();
	}
}