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)

def div_count(n, k, l)
  (n / k) + (n / l) - (n / k.lcm(l))
end

def main(argv)
  (a, b, c, d) = gets.chomp.split(' ').map(&:to_i)
  
  m = b - a + 1
  x = div_count(a - 1, c, d)
  y = div_count(b, c, d)
  p (m - (y - x))
end

if self.to_s == 'main' then
  main(ARGV)
end