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)

#include <iostream>
#include <algorithm>
#include <map>
#include <vector>
#include <set>
#include <bitset>
#include <unordered_map>
#include <queue>
#include <cstring>

using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repn(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define MOD 1000000008

int gcd(int a, int b){
    if( a < b){
        swap(a,b);
    }
    return (a % b == 0)? b:gcd(a, a%b);
}

int lcm(int a, int b){
    return (a*b)/gcd(a,b);
}

int main(){
    ll n, d, a;
    cin >> n >> d >> a;

    map<ll, ll> monsters;
    rep(i,n){
        ll pos, hp;
        cin >> pos >> hp;
        monsters.insert(make_pair(pos, hp));
    }

    unordered_map<ll, ll> current_bombs;
    ll ans = 0;

    for(pair<ll, ll> monster : monsters){
        for(auto bomb = current_bombs.begin(); bomb != current_bombs.end();){
            if( bomb->first < monster.first ){
                bomb = current_bombs.erase(bomb);
            } else {
                monster.second -= bomb->second * a;
                bomb++;
            }
        }

        if( monster.second > 0 ) {
            ll num_bomb = monster.second / a + !(monster.second % a == 0);
            ans += num_bomb;
            current_bombs.insert(make_pair(monster.first + (d*2), num_bomb));
        }
    }
    cout << ans << endl;
}