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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
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();
		System.out.println(solve(b,c,d)-solve(a-1,c,d));

	}
	static long gcd(long a,long b) {
		if(b==0) {
			return a;
		}
		return gcd(b,a%b);
	}
	static long solve(long b,long c,long d) {
		long ret = b;
		long other = c*d/gcd(c,d);
		ret-= b/c;
		ret -= b/d;
		ret += b/other;
		return ret;
	}

}