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
#include<iostream>
using namespace std;
long gcd(long m,long n){if(!n)return m;return gcd(n,m%n);}
long lcm(long m,long n){return m*n/gcd(m,n);}
int main()
{
	long a,b,c,d;
	cin>>a>>b>>c>>d;
	a--;
	cout<<b-a-b/c+a/c-b/d+a/d+b/lcm(c,d)-a/lcm(c,d)<<endl;
	return 0;
}