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)


object Main extends App {
  import scala.io.StdIn._
  val Array(a, b, c, d) = readLine.trim.split(' ').map(_.toLong)
  val lower = (a - 1) - (a - 1) / c - (a - 1) / d + (a - 1) / lcm(c, d)
  val upper = b - b / c - b / d + b / lcm(c, d)
  println(upper - lower)
  def gcd(a: Long, b: Long): Long = {
    b match {
      case 0 => a
      case _ => gcd(b, a % b)
    }
  }
  def lcm(a: Long, b: Long): Long = {
    a / gcd(a, b) * b
  }
}