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.*;
/**
 * Main
 */
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 l = lcm(C,D);
        long val1 = B - (B/C + B/D) + B/l;
        long val2 = (A-1) - ((A-1)/C + (A-1)/D) + (A-1)/l;
        System.out.println(val1-val2);
        sc.close();
    }

    //b < a
    static long gcd(long a, long b) {
        if (a == 0 || b == 0) return b+a;
        else return gcd(b,a%b);
    }

    static long lcm(long a, long b) {
        if(a <= b) {
            long tmp = a;
            a = b;
            b = tmp;
        }
        return a*b/gcd(a,b);
    }
}