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 cd = gcd(c, d);

		long cdd = c / cd * d;

		long e = b / c - a / c + b / d - a / d - b / cdd + a / cdd;

		if (a % c == 0)
			e++;
		if (a % d == 0)
			e++;
		if (a % cdd == 0)
			e--;

		System.out.println(b - a + 1 - e);

	}

	static long gcd(long l, long m) {
		long n = l;
		if (l < m) {
			l = m;
			m = n;
		}

		while (m != 0) {
			n = m;
			m = l % m;
			l = n;
		}

		return l;
	}

}