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 inputs = readInputLine().split(" ").map { it.toLong() }
    
    val a = inputs[0]
    val b = inputs[1]
    val c = inputs[2]
    val d = inputs[3]
    
    val cdgcd = 
        if (c > d) {
            gcd(c, d)
        } else {
            gcd(d, c)
        }
    val cdlcm = c * d / cdgcd

    var res = b - a + 1

    if (b / c != a / c) {
        res -= b / c - a / c
    }
    if (a % c == 0L) {
        res--
    }
    
    if (b / d != a / d) {
        res -= b / d - a / d
    }
    if (a % d == 0L) {
        res--
    }
    
    if (b / cdlcm != a / cdlcm) {
        res += b / cdlcm - a / cdlcm
    }
    if (a % cdlcm == 0L) {
        res++
    }

    println("$res")
}
 
fun readInputLine(): String {
    return readLine()!!
}

fun gcd(a: Long, b: Long): Long {
    // a >= b とする
    if (b == 0L) {
        return a
    }
    return gcd(b, a % b)
}