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 gcd(long long x,long long y){
    if(y==0)
        return x;
    else
        return gcd(y,x%y);
}

int main(){
    long long a,b,c,d;
    cin>>a>>b>>c>>d;
    a-=1;
    cout<<b-b/c-b/d+b/(c*d/gcd(c,d))-(a-a/c-a/d+a/(c*d/gcd(c,d)));
}



