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();
		long B = sc.nextLong();
		long C = sc.nextLong();
		long D = sc.nextLong();
		sc.close();

		// Cで割り切れる数
		long divideC = (B / C) - ((A - 1) / C);
		// Dで割り切れる数
		long divideD = (B / D) - ((A - 1) / D);
		// CとDの最小公倍数で割り切れる数
		long lcm = calcLcm(C, D);
		long divideLcm = (B / lcm) - ((A - 1) / lcm);
		System.out.println((B - (A - 1)) - (divideC + divideD - divideLcm));
	}

	// 最大公約数を求める。
	public static long calcGcd(long m, long n) {
		if (m < n) {
			long tmp = m;
			m = n;
			n = tmp;
		}
		long remainder = 0;
		while ((remainder = m % n) != 0) {
			m = n;
			n = remainder;
		}
		return n;
	}

	// 最小公倍数を求める。
	public static long calcLcm(long m, long n) {
		return m * n / calcGcd(m, n);
	}
}