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)

tailrec fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)

fun main(args: Array<String>) {
    val (a,b,c,d) = readLine()!!.split(" ").map { it.toLong() }
    val bc = b/c
    val bd = b/d
    val ac = (a-1)/c
    val ad = (a-1)/d
    val bcd = b/( c/gcd(c,d)*d )
    val acd = (a-1)/( c/gcd(c,d)*d )
    println(b-(a-1) -(bc-ac) -(bd-ad) +(bcd-acd))
}