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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
long long int x[200005], h[200005];
int asc(const void* a, const void* b)
{
	if (x[*(long long int*)a] > x[*(long long int*)b])return 1;
	if (x[*(long long int*)a] < x[*(long long int*)b])return -1;
	return 0;
}
long long int fmax(long long int a, long long int b)
{
	if (a > b)
		return a;
	else
		return b;
}
long long int seg[800005], ss;
void getmax(long long int a, long long int k, long long int l, long long int r)
{
	if (2 * k + 2 < 2 * ss - 1)
	{
		seg[2 * k + 1] += seg[k];
		seg[2 * k + 2] += seg[k];
		seg[k] = 0;
	}
	if (a < l || r <= a)
		return;
	if (l + 1 == r)
		return;
	if ((r + l) / 2 > a)
		getmax(a, 2 * k + 1, l, (l + r) / 2);
	else
		getmax(a, 2 * k + 2, (l + r) / 2, r);
	return;
}
void set(long long int a, long long int b, long long int x, long long int k, long long int l, long long int r)
{
	if (r <= a || b <= l)
		return;
	if (a <= l && r <= b)
	{
		seg[k] -= x;
		return;
	}
	set(a, b, x, 2 * k + 1, l, (l + r) / 2);
	set(a, b, x, 2 * k + 2, (l + r) / 2, r);
	return;
}
int main()
{
	long long int n, d, a;
	scanf("%lld %lld %lld", &n, &d, &a);
	long long int i;
	for (i = 0; i < n; i++)
		scanf("%lld %lld", &x[i], &h[i]);
	long long int c[200005];
	for (i = 0; i < n; i++)
		c[i] = i;
	qsort(c, n, sizeof(long long int), asc);
	ss = 1;
	while (ss < n)
		ss *= 2;
	for (i = 0; i < 2 * ss - 1; i++)
		seg[i] = 0;
	for (i = 0; i < n; i++)
		seg[i + ss - 1] = h[c[i]];
	int min, mid, max;
	long long int ans = 0;
	for (i = n - 1; i >= 0; i--)
	{
		getmax(i, 0, 0, ss);
		if (seg[i + ss - 1] < 0)
			seg[i + ss - 1] = 0;
		ans += (seg[i + ss - 1] + a - 1) / a;
		min = 0;
		max = i;
		while (max - min > 1)
		{
			mid = (max + min) / 2;
			if (x[c[mid]] + 2 * d < x[c[i]])
				min = mid;
			else
				max = mid;
		}
		if (x[c[min]] + 2 * d < x[c[i]])
			min++;
		set(min, i + 1, (seg[i + ss - 1] + a - 1) / a * a, 0, 0, ss);
	}
	printf("%lld\n", ans);
	return 0;
}