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;
int main(){
	long long a,b,c,d,dc,dd,e,GCM=1,i,ans;
	cin>>a>>b>>c>>d;
	dc=c;
	dd=d;
	for(i=10000;i!=1;i--){
		if(dc%i==0&&dd%i==0){
			dc/=i;
			dd/=i;
			GCM*=i;
		}
	}
	e=dc*dd*GCM;
	a--;
	ans=b-a;
	ans-=b/c+b/d-b/e;   
	ans+=a/c+a/d-a/e;
	cout<<ans;
	
}