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

  total = b - a + 1

  ac = a - a % c
  bc = b - b % c
  n = bc - ac
  ccnt = n / c
  ccnt += 1 if a % c == 0

  ad = a - a % d
  bd = b - b % d
  m = bd - ad
  dcnt = m / d
  dcnt += 1 if a % d == 0

  lcm = c.lcm(d)
  al = a - a % lcm
  bl = b - b % lcm
  o = bl - al
  cnt = o / lcm
  cnt += 1 if a % lcm == 0

  puts total - ccnt - dcnt + cnt
end

main if $0 == __FILE__