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;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long A = sc.nextLong();
        long B = sc.nextLong();
        int C = sc.nextInt();
        int D = sc.nextInt();
        int g = C > D ? gcd(C, D) : gcd(D, C);
        long k = (long) C*D/g;
        long result = B - (B/C + B/D - B/k) - (A-1 - ((A-1)/C + (A-1)/D - (A-1)/k));
        System.out.println(result);
    }

    private static int gcd(int a, int b) {
        int temp = 0;
        while (a % b != 0) {
            temp = a;
            a = b;
            b = temp % b;
        }
        return b;
    }
}