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.*;
import java.util.stream.*;

public class Main {
  public static void main(String[] args) throws Exception {
    Scanner in = new Scanner(System.in);
    long A = in.nextLong(), B = in.nextLong(), C = in.nextLong(), D = in.nextLong();
    System.out.println((B - A + 1) - calc(A, B, C) - calc(A, B, D) + calc(A, B, lcm(C, D)));
  }

  public static long calc(long a, long b, long c) {
    return b / c - (a - 1) / c;
  }

  public static long gcd(long x, long y) {
    return y == 0 ? x : gcd(y, x % y);
  }

  public static long lcm(long x, long y) {
    return x * (y / gcd(x, y));
  }
}