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 zhan(int x,int y){
	if(x<y) swap(x,y);
	if(x%y!=0) return zhan(y,x%y);
	return y;
}
int main(){
	long long a,b,c,d;
	cin>>a>>b>>c>>d;
	long long x=c*d/zhan(c,d);
	cout<<(b-a+1)-(b/c-(a-1)/c)-(b/d-(a-1)/d)+(b/x-(a-1)/x);
	return 0;
}