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 (Clang 10.0.0) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdbool.h>
#define MOD 1000000007

typedef long long ll;

typedef struct pair {
    ll x, h;
}pair;

int asc(const void* a, const void* b) { return *(int*)a - *(int*)b; }

ll max(ll x, ll y) { return (x > y) ? x : y; }

ll min(ll x, ll y) { return (x < y) ? x : y; }

int main() {
    ll n, d, a;
    pair monster[200001];
    scanf("%lld%lld%lld", &n,&d,&a);
    ll X, H;
    for (ll i = 0; i < n; i++) {
        scanf("%lld%lld", &X, &H);
        monster[i].x = X;
        monster[i].h = (H - 1) / a + 1;
    }
    qsort(monster, n, sizeof(pair), asc);
    ll arr[200001] = {}, r = 0, ans = 0;
    for (ll l = 0; l < n; l++) {
        if (l) arr[l] += arr[l - 1];
        if (monster[l].h <= arr[l]) continue;
        while (r < n && monster[r].x - monster[l].x <= 2 * d) r++;
        ll cnt = monster[l].h - arr[l];
        ans += cnt;
        arr[l] += cnt;
        arr[r] -= cnt;
    }
    
    printf("%lld", ans);

    return 0;
}