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 {

    long INF = Long.MAX_VALUE;
    long[][] dp;
    int MAX_M = 100000;
    int MAX_N = 100000;

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

    void solve() {
        Scanner sc = new Scanner(System.in);
        long A = sc.nextLong();
        A--;
        long B = sc.nextLong();
        long C = sc.nextLong();
        long c = (B/C) - (A/C);
        long D = sc.nextLong();
        long d = (B/D) - (A/D);
        long L = lcm(C,D);
        long l = (B/L) - (A/L);
        System.out.println((B-A)-c-d+l);

    }
    static long lcm (long a, long b) {
	long temp;
	long c = a;
	c *= b;
	while((temp = a%b)!=0) {
		a = b;
		b = temp;
	}
	return (c/b);
}
}