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.nextLong()
    val b = sc.nextLong()
    val c = sc.nextLong()
    val d = sc.nextLong()
    println(problem131c(a, b, c, d))
}

fun problem131c(a: Long, b: Long, c: Long, d: Long): Long {
    fun computeGreatestCommonDivisor(small: Long, big: Long): Long {
        val rest = small % big
        return if (rest == 0L) big else computeGreatestCommonDivisor(big, rest)
    }
    val bMultiple = b / c + b / d
    val aMultiple = (a - 1) / c + (a - 1) / d
    val greatestCommon = if (c > d) {
        computeGreatestCommonDivisor(c, d)
    } else {
        computeGreatestCommonDivisor(d, c)
    }
    val leastCommon = c * d / greatestCommon
    var bAns = b - bMultiple
    bAns += b / leastCommon
    var aAns = (a - 1) - aMultiple
    aAns += (a - 1) / leastCommon
    return bAns - aAns
}