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 {

	static long a, b;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		a = sc.nextLong();
		b = sc.nextLong();
		long c = sc.nextLong();
		long d = sc.nextLong();

		System.out.println(b - a + 1 - (calc(c) + calc(d) - calc(lcm(c, d))));

	}

	static long calc(long divide) {
		return b / divide - (a - 1) / divide;
	}

	static long gcd(long m, long n) {
		if (m < n)
			return gcd(n, m);
		if (n == 0)
			return m;
		return gcd(n, m % n);
	}

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

}