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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    static long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}
    static long lcm (long a, long b) {return a*b/gcd(a,b);}

    
    public static void main(String args[]) {

        Scanner sc = new Scanner(System.in);
        long A = sc.nextLong()-1;
        long B = sc.nextLong();
        long C = sc.nextLong();
        long D = sc.nextLong();
        
        long cc = (B/C)-(A/C);
        long dc = (B/D)-(A/D);
        long lcm = lcm(C, D);
        
        long ccd = (B/lcm)-(A/lcm);
        System.out.println(B-A-cc-dc+ccd);
    }
}