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 {

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)
    val A, B, C, D = sc.nextLong

    def gcd(x: Long, y: Long): Long = {
      if (y == 0) x else gcd(y, x % y)
    }

    val lcm = C * D / gcd(C, D)
    val divideA = (A - 1) - ((A - 1) / C + (A - 1) / D - (A - 1) / lcm)
    val divideB = B - (B / C + B / D - B / lcm)
    println(divideB - divideA)
  }
}