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();
		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)));
	}
	static long gcd(long C,long D){
		long dai=Math.max(C,D);
		long shou=Math.min(C,D);
		long amari=dai%shou;
		while(amari!=0){
			dai=shou;
			shou=amari;
			amari=dai%shou;
		}
		return shou;
	}
	static long lcm(long C,long D){
		return C*D/gcd(C,D);
	}
}


