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.

Examples

Input

4 9 2 3


Output

2


Input

10 40 6 8


Output

23


Input

314159265358979323 846264338327950288 419716939 937510582


Output

532105071133627368
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();
    long c = sc.nextInt();
    long d = sc.nextInt();

    long lcmCD = lcm(c, d);

    long cMultiples = b / c - (a - 1) / c;
    long dMultiples = b / d - (a - 1) / d;
    long cdMultiples = b / lcmCD - (a - 1) / lcmCD;

    System.out.println(b - a + 1 - cMultiples - dMultiples + cdMultiples);
  }

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

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