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 Ruby (2.3.3) (judge verdict: Accepted)


class BIT
  attr_reader :tree

  def initialize(n)
    @tree = Array.new(n + 1, 0)
  end

  def add(i, diff)
    while i < @tree.size
      @tree[i] += diff
      i += (i & -i)
    end
  end

  def sum(i)
    t = 0
    while i > 0 do
      t += @tree[i]
      i -= (i & -i)
    end
    return t
  end

  def [](i)
    s = @tree[i]
    if i > 0
      z = i - (i & -i)
      y = i - 1
      while y != z
        s -= @tree[y]
        y -= (i & -i)
      end
    end
    return s
  end
end


n, d, a = gets.chomp.split.map(&:to_i)

ms = []
n.times do
  ms.push gets.chomp.split.map(&:to_i)
end
ms = ms.sort_by { |x| x[0] }
ms.push [1<<60, 0]

dst = {}
(n).times do |i|
  x, _ = *ms[i]
  r = x + 2*d
  k = ms.bsearch_index { |m| m[0] > r }
  dst[i] = k
end

bit = BIT.new(n+1)

res = 0
n.times do |i|
  x, h = *ms[i]
  t = bit.sum(i + 1)
  h -= t
  next if h <= 0

  cnt = (h + a - 1) / a
  res += cnt
  damage = cnt * a

  bit.add(i + 1, damage)
  bit.add(dst[i] + 1, -damage)
end

puts res