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)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val a = sc.next().toLong()
    val b = sc.next().toLong()
    val c = sc.next().toLong()
    val d = sc.next().toLong()

    println(abc131c(a, b, c, d))
}

private fun abc131c(a: Long, b: Long, c: Long, d: Long): Long {
    var l = lcm(c, d)

    var ans = b - a + 1
    ans -= (b / c) + (b / d) - (b / l)
    ans += ((a - 1) / c) + ((a - 1) / d) - ((a - 1) / l)

    return ans
}

private fun lcm(a: Long, b: Long): Long {
    return a / gcd(a, b) * b
}

private fun gcd(a: Long, b: Long): Long {
    if (b > 0) {
        return gcd(b, a % b)
    }
    return a
}