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>) {
    fun gcd(a: Long, b: Long): Long {
        return if (b > 0) gcd(b, a % b) else a
    }
    val (a, b, c, d) = readLine()!!.split(' ').map(String::toLong)
    var total = b - a + 1
    total -= b / c
    total += (a - 1) / c
    total -= b / d
    total += (a - 1) / d
    total += b / (d * c / gcd(d,c))
    total -= (a - 1) / (d * c / gcd(d,c))

    println(total)
}