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>) {

    val calc = { N: Long, L: Long, U: Long ->
        //        println(N)
//        println("($N - ($N / $L + $N / $U - $N / ($L * $U)))")
        (N - (N / L + N / U - N / lcm(L, U)))
    }

    val (A, B, C, D) = readLine()!!.split(" ").map(String::toLong)


//    println(calc(B, C, D))
//    println(calc(A - 1, C, D))
    println(calc(B, C, D) - calc(A - 1, C, D))
}

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

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