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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        
        Scanner sc = new Scanner(System.in);
        
        long A = sc.nextLong();
        long B = sc.nextLong();
        long C = sc.nextLong();
        long D = sc.nextLong();
        
        System.out.println( f(B, C, D) - f(A - 1, C, D) );
        
    }
    
    // x以下でcまたはdで割り切れない数の個数
    public static long f(long x, long c, long d){
        return x - x / c - x / d + x / LCM(c, d);
    }
    
    public static long GCD(long a, long b){
        if ( b == 0 ) return a; 
        return GCD(b, a % b);
    }
    
    public static long LCM(long a, long b){
        return a * b / GCD(a, b);
    }
}