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.*;
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();
    long E =(A-1)/C;long F =B/C;
    long G =(A-1)/D;long H =B/D;
    long I =C*D;
    long s =C%D;
    while(s!=0){
      s=C%D;
      C=D;
      D=s;}
    long J =I/C;
    long K =(A-1)/J;long L =B/J;
    long ans =B-A+1-F+E+G-H+L-K;
    System.out.println(ans);
  }
}