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.Arrays;
import java.util.Scanner;

public class Main {
    void run() {
        Scanner sc = new Scanner(System.in);

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

        long countC = b / c - a / c + (a % c == 0 ? 1 : 0);
        long countD = b / d - a / d + (a % d == 0 ? 1 : 0);
        long cd = lcm(c, d);
        long countCD = b / cd - a / cd + (a % cd == 0 ? 1 : 0);
        System.out.println(b - a + 1 - countC - countD + countCD);
    }

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

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


    public static void main(String[] args) {
        new Main().run();
    }
}