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;
import java.util.stream.LongStream;

public class Main {
    public static Long gcd(Long a, Long b) {
        if (a < b) return gcd(b, a);
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    public static Long lcm(Long a, Long b) {
        if (a < b) return lcm(b, a);
        return a * b / gcd(a, b);
    }

    public static Long cal(Long a, Long b) {
        Long min_f;
        if(a%b == 0) {
            min_f = a / b;
        } else {
            min_f= (a / b) + 1;
        }
        return min_f;

    }
    public static void main(String[] args) {
        //コード
        Scanner scanner = new Scanner(System.in);
        Long a = scanner.nextLong();
        Long b = scanner.nextLong();
        Long c = scanner.nextLong();
        Long d = scanner.nextLong();

        Long a_b_min = cal(a,c);
        Long a_b_max = b / c;
        Long total1 = (a_b_max - a_b_min) + 1;

        Long a_d_min = cal(a,d);
        Long b_d_max = b / d;
        Long total2 = (b_d_max - a_d_min) + 1;

        Long lcm = lcm(c,d);
        Long lcm_min = cal(a,lcm);
        Long lcm_max = b / lcm;
        Long total3 = (lcm_max - lcm_min) + 1;

        System.out.println((b-a+1) - (total1+total2-total3));


    }
}