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 long gcd(long a, long b) {
		return b == 0 ? a: gcd(b, a % b);
	}
	
	public static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long A = sc.nextLong();
		long B = sc.nextLong();
		long C = sc.nextInt();
		long D = sc.nextInt();
		System.out.println((B-A+1)-B/C+(A-1)/C-B/D+(A-1)/D+B/lcm(C,D)-(A-1)/lcm(C,D)); 
	}

}
