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)

require 'prime'
a, b, c, d = gets.split.map(&:to_i)

def m(a, b, x)
  s = (a-1)/x + 1
  e = b/x
  e-s+1
end

cs = m(a, b, c)
ds = m(a, b, d)
cds = m(a, b, c.lcm(d))

puts (b - a + 1) - (cs + ds) + cds