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.*;

class Main{
	public static void main(String[] $){
		Scanner s=new Scanner(System.in);

		long a=s.nextLong()-1;
		long b=s.nextLong();
		long c=s.nextLong();
		long d=s.nextLong();

		long w=b-a;
		System.err.println(w);
		long x=b/c-a/c;
		System.err.println(x);
		long y=b/d-a/d;
		System.err.println(y);
		long z=b/gcd(c,d)-a/gcd(c,d);
		System.err.println(z);
		System.out.println(w-x-y+z);
	}

	private static long gcd(long c,long d){
		return c*d/lcm(c,d);
	}

	private static long lcm(long c,long d){
		return d==0?c:lcm(d,c%d);
	}
}