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 (A, B, C, D) = readLine()!!.split(" ").map(String::toLong)
    val c = B / C - (A - 1) / C
    val d = B / D - (A - 1) / D
    val cd = B / lcm(C, D) - (A - 1) / lcm(C, D)
    println(B - (A - 1) - c - d + cd)
}

// 最小公倍数
fun lcm(a: Long, b: Long): Long {
    return a / gcd(a, b) * b
}

// 最大公約数
tailrec fun gcd(a: Long, b: Long): Long {
    if (a < b) return gcd(b, a)
    if (b == 0L) return a
    if (a <= 0L) throw IllegalArgumentException()
    return gcd(b, a % b)
}