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.io.InputStream;
import java.io.PrintStream;
import java.util.*;

public class Main {

  public static void main(String[] args) {
    solve(System.in, System.out);
  }

  private static final long MOD = 1000000007L;


  static void solve(InputStream is, PrintStream os) {
    Scanner sc = new Scanner(is);

    /* read */
    long a = sc.nextLong();
    long b = sc.nextLong();

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

    a--;

    long cumA = a - (a / c + a / d - a / lcm(c, d));
    long cumB = b - (b / c + b / d - b / lcm(c, d));

    os.println(cumB - cumA);
  }

  static long lcm(long a, long b) {
    return a / gcd(a, b) * b;
  }

  static long gcd(long a, long b) {
    long r;
    while( (r = a % b) != 0 ) {
      a = b;
      b = r;
    }
    return b;
  }
}