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.*;

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

        long a = sc.nextLong() - 1;
        long b = sc.nextLong();
        long c = sc.nextLong();
        long d = sc.nextLong();

        long x = lcm(c, d);

        long modB = b - b / c - b / d + b / x;
        long modA = a - a / c - a / d + a / x;

        System.out.println(modB - modA);

    }

    static long lcm (long a, long b) {
        long temp;
        long c = a;
        c *= b;
        while((temp = a%b)!=0) {
            a = b;
            b = temp;
        }
        return c/b;
    }

}