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.Arrays;
import java.util.Scanner;

public class Main {

    long MOD = (long)1e9 + 7;

    void run() {
        Scanner sc = new Scanner(System.in);
        long a = sc.nextLong(), b = sc.nextLong();
        long c = sc.nextInt(), d = sc.nextInt();
        long m = lcm(c, d);
        long cntc = b / c - (a - 1) / c;
        long cntd = b / d - (a - 1) / d;
        long cntcd = b / m - (a - 1) / m;
        debug(cntc, cntd, cntcd);
        System.out.println(b - a + 1 - (cntc + cntd - cntcd));
    }

    long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

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

    void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
