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.*;
import java.lang.*;
import java.io.*;

public class Main{	
public static void main (String[] args){
	Scanner sc = new Scanner(System.in);
	long a = Long.parseLong(sc.next());
	long b = Long.parseLong(sc.next());
	long c = Long.parseLong(sc.next());
	long d = Long.parseLong(sc.next());
	long s = 0;
	
	
	if(c!=d){
		long z = lcm(c,d);
		long x = b/c - (a-1)/c;   
		long y = b/d - (a-1)/d;
		long w = b/z - (a-1)/z;
		s = b-a+1-x-y+w;
	}else{
		long x = b/c - (a-1)/c;
		s = b-a+1-x;
	}	
	
	
	System.out.println(s);
}
private static long lcm(long a, long b){ 	
	return a*b/gcd(a,b);
}
private static long gcd(long a, long b){
	if(a<b) return gcd(b,a);
	if(b==0)return a;
	return gcd(b,a%b);
}
}
