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.*;

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_sum=B-A+1;
		long ans_div_c=B/C-A/C;
		long ans_div_d=B/D-A/D;
		long cd=C*D/gcd(C,D);
		long ans_div_cd=B/cd-A/cd;
		if (A%C==0) {
			ans_div_c+=1;
		}
		if (A%D==0) {
			ans_div_d+=1;
		}
		if (A%cd==0) {
			ans_div_cd+=1;
		}
		System.out.println(ans_sum-ans_div_c-ans_div_d+ans_div_cd);
	}

	static long gcd(long a,long b) {
	    long temp;
	    while ((temp=a%b)!=0) {
	        a=b;
	        b=temp;
	    }
	    return b;
	}
}