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 static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		long a = sc.nextLong();
		long b = sc.nextLong();
		long c = sc.nextLong();
		long d = sc.nextLong();
		
		// 計算
		long result = 0;
		long c0 = b/c - (a-1)/c;
		long d0 = b/d - (a-1)/d;
		long l = lcm(c, d);
		long cd0 = b/l - (a-1)/l;
		result = (b - a + 1) - (c0 + d0 - cd0);

		// 出力
		System.out.println(result);
		
	}
	
	static long gcd(long x, long y){
	    if(x < y){
	        long temp = x;
	        x = y;
	        y = temp;
	    }
	    if(x%y == 0) return y;
	    return gcd(y , x%y);
	}
	
	static long lcm(long x, long y){
	    return x*y/gcd(x, y);
	}
}
