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<bits/stdc++.h>
using namespace std;
long long a,b,c,d,e,f,ans;
long long gcd(int x,int y){
    if(y==0) return x;
    return gcd(y,x%y);
}
int main(){
	cin>>a>>b>>c>>d;
	cout<<b-a+1-(b/c-a/c)-(b/d-a/d)+(b/(c/gcd(c,d)*d)-a/(c/gcd(c,d)*d))-(a%c==0)-(a%d==0)+(a%(c/gcd(c,d)*d)==0)<<endl;
	return 0;
}