Problem:
Score : 300 points

Problem Statement

You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Constraints

1\leq A\leq B\leq 10^{18}

1\leq C,D\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Sample Input 1

4 9 2 3

Sample Output 1

2

5 and 7 satisfy the condition.

Sample Input 2

10 40 6 8

Sample Output 2

23

Sample Input 3

314159265358979323 846264338327950288 419716939 937510582

Sample Output 3

532105071133627368

Solution in Ruby (2.3.3) (judge verdict: Accepted)

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

c_num = (b / c) - (a / c)
c_num += 1 if a % c == 0
d_num = (b / d) - (a / d)
d_num += 1 if a % d == 0

# 最小公倍数
e = [c, d].max
f = [c, d].min

p = e * f

while true do
  # q = e / f
  r = e % f
  if r == 0
    p = f
    break
  end

  e = f
  f = r
end

g = c / p * d

g_num = (b / g) - (a/ g)
g_num += 1 if a % g == 0
puts b - a + 1 - (c_num + d_num - g_num)