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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    var (A, B, C, D) = listOfLong()
    A -= 1
    val e = lcm(C, D)
    val ac = A / C
    val ad = A / D
    val acd = A / e
    val a = ac + ad - acd
    val bc = B / C
    val bd = B / D
    val bcd = B / e
    val b = bc + bd - bcd
    val ab = b - a
    val ans = (B - A) - ab
    println(ans)
}
fun gcd(a: Long, b: Long): Long = if (a % b == 0L) b else gcd(b, a % b)
fun lcm(a: Long, b: Long): Long = a * b / gcd(a, b)
fun next() = readLine()!!
fun listOfString() = next().split(" ")
fun listOfLong() = listOfString().map { java.lang.Long.parseLong(it) }