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: Accepted)

import scala.io.StdIn._
object Main extends App {
  val Array(a, b, c, d) = readLine.split(" ").map(_.toLong)
  def gcd(l: Long, r: Long): Long = if (l % r == 0) r else gcd(r, l % r)
  val lcm = c * d / gcd(c, d)
  def num(div: Long): Long = b / div - (a - 1) / div
  println(b - (a - 1) - (num(c) + num(d) - num(lcm)))
}