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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
N,d,a = map(int,readline().split())

data0 = [0]*(N+1)
data1 = [0]*(N+1)
# 区間[l, r)に x を加算
def _add(data, k, x):
    while k <= N:
        data[k] += x
        k += k & -k
def add(l, r, x):
    _add(data0, l, -x*(l-1))
    _add(data0, r, x*(r-1))
    _add(data1, l, x)
    _add(data1, r, -x)

# 区間[l, r)の和を求める
def get(data, k):
    s = 0
    while k:
        s += data[k]
        k -= k & -k
    return s
def query(l, r):
  return get(data1,r-1)*(r-1)+get(data0,r-1)-get(data1,l-1)*(l-1)-get(data0,l-1)

xh = []
for _ in range(N):
    x,h = map(int,readline().split())
    xh.append((x,h))

xh = sorted(xh)
xl = [x for x,h in xh]

for i in range(N):
    add(i+1, i+2, xh[i][1])

import bisect,math

ans = 0
for i in range(N):
    hp = query(i + 1, i + 2)
    #print(data0,data1,hp)    
    if hp > 0:
        count = math.ceil(hp/a)
        ans += count
        damage = count * a
        idx = bisect.bisect_right(xl, xl[i] + 2*d)
        add(i+1, idx+1, -damage)
print(ans)