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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends App {
  val in         = new java.util.Scanner(System.in)
  val a, b, c, d = in.nextLong

  def count(now: Long, limit: Long, dividers: Seq[Long], counter: Long): Long =
  if (now > limit)
    counter
  else
    if (dividers.forall(now % _ != 0))
      count(now + 1, limit, dividers, counter + 1)
    else
      count(now + 1, limit, dividers, counter)

  val answer = count(a, b, Seq(c, d), 0)

  println(answer)
}