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 ans = (B / C - (A - 1) / C) + (B / D - (A - 1) / D) - (B / lcm(C, D) - (A - 1) / lcm(C, D));
		System.out.println(B - A - ans + 1);
	}
	
	static long lcm(long m, long n) {
	    return m * n / gcd(m, n);
	}

	static long gcd (long a, long b) {
		return b > 0 ? gcd(b, a % b) : a;
	}
}
