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();
        int c = sc.nextInt();
        int d = sc.nextInt();

        long ans = f(b, c, d) - f(a - 1, c, d);
        System.out.println(ans);
    }

    static long f(long x, long c, long d) {
        long ret = x; // これが全体数
        ret -= (x / c); // Cで割れる数を減らす
        ret -= (x / d); // Dで割れる数を減らす
        ret += x / lcm(c, d); // CとDで重複して減らした数を加算する
        return ret;
    }

    static long lcm(long a, long b) {
        // 最小公倍数
        return (a * b) / gcd(a, b);
    }

    static long gcd(long a, long b) {
        // 最大公約数
        return b == 0 ? a : gcd(b, a % b);
    }
}