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 {
	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 E = lcm(C,D);

		long x = 0;
		long y = 0;
		long z = 0;

		if (A%C == 0){
			x = B/C - A/C + 1;
		} else {
			x = B/C - A/C;
		}

		if (A%D == 0){
			y = B/D - A/D + 1;
		} else {
			y = B/D - A/D;
		}

		if (A%E == 0){
			z = B/E - A/E + 1;
		} else {
			z = B/E - A/E;
		}

		System.out.println(B - A + 1 - (x + y - z));
	}

	public static long gcd(long a , long b) {
		if (b==0) {
			return a;
		}
		return gcd(b,a%b);
	}

	private static long lcm(long m, long n) {
        return m * n / gcd(m, n);
    }
}