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 {

	// c < d
	public static long eukleides(long c, long d){
		if(d % c == 0){
			return c;
		}

		long mod = d % c;

		return eukleides(mod, c);
	}

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);

		// input
		long a = scan.nextLong();
		long b = scan.nextLong();
		long c = scan.nextInt();
		long d = scan.nextInt();
		if(c > d){
			long temp = c;
			c = d;
			d = temp;
		}

		long gcd = eukleides(c, d);
		long lcm = (c * d) / gcd;
		long answer = b - b / c - b / d + b / lcm;
		answer -= a - 1 - (a - 1) / c - (a - 1) / d + (a - 1) / lcm;

		System.out.println(answer);

	}
}