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) {
 
    Scanner sc = new Scanner(System.in);
    long A = sc.nextLong();
    long B = sc.nextLong();
    long C = sc.nextLong();
    long D = sc.nextLong();
 
    long lcm = (C * D) / gcd(D, C);
    
    System.out.println(count(B, C, D, lcm) - count(A-1, C, D, lcm));
  }
  
  private static long gcd(long a, long b) {
    if (b == 0) {
      return a;
    }
    return gcd(b, a%b);
  }
  
  private static long count(long n, long C, long D, long lcm) {
    return n - n/C - n/D + n/lcm;
  }
}