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 num1,num2,num3,num4,num5,num6,opt;
        long cd = C*D/gcd(C,D);
        num1 = B/C;
        num2 = B/D;
        num3 = B/cd;
        num4 = (A-1)/C;
        num5 = (A-1)/D;
        num6 = (A-1)/cd;
        opt = (B-A+1)-(num1+num2-num3-(num4+num5-num6));
        System.out.println(opt);
    }
    private static long gcd(long m, long n) {
        if(m < n) return gcd(n, m);
        if(n == 0) return m;
        return gcd(n, m % n);
    }
}
