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.Scanner;

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 cnum = (B/C) - ((A-1)/C);
		long dnum = (B/D) - ((A-1)/D);
		long cdnum =(B/lcm(C,D)) - ((A-1)/lcm(C,D));

		long ans = (B-A+1) - (cnum + dnum - cdnum);
		System.out.println(ans);
	}

	//整数a,bの最大公約数
	public static long gcd(long a,long b) {
		if(b == 0) return a;
		else return gcd(b,a%b);
	}

	//整数a,bの最小公倍数
	public static long lcm(long a,long b) {
		return a*b/gcd(a,b);
	}
}
