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)

lcm = C.lcm(D)
primes = B - A

div_candidates = [C, D, lcm].map { |i|
  size = B - A + 1
  times = size / i
  offset = i - A % i
  times + (size%i > offset ? 1 : 0)
}

size = B - A + 1
size -= div_candidates[0]
size -= div_candidates[1]
size += div_candidates[2]

puts size