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>) = println(run {
    val (a,b,c,d) = readLine()!!.split(" ").map { it.toLong() }
    fun count(x: Long) = x - x/c - x/d + x/((c*d)/gcd(c,d))
    count(b)-count(a-1)
})

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