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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func GCD(a, b int) int {
        for b != 0 {
                t := b
                b = a % b
                a = t
        }
        return a
}

func LCM(a, b int, integers ...int) int {
        result := a * b / GCD(a, b)

        for i := 0; i < len(integers); i++ {
                result = LCM(result, integers[i])
        }

        return result
}

func main() {
        var a, b, c, d int
        fmt.Scan(&a, &b, &c, &d)

        e := LCM(c, d)
        sum := b/c - (a-1)/c + b/d - (a-1)/d - (b/e - (a-1)/e)
        fmt.Println(b - a + 1 - sum)
}