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;
int mygcd(int64_t a,int64_t b){
    if(a%b==0) return b;
    else return (mygcd(b,a%b));
}
int main(){
    int64_t A,B,C,D;
    cin>>A>>B>>C>>D;
    cout<<B-(B/C)-(B/D)+B/((C*D)/mygcd(C,D))-((A-1)-(A-1)/C-(A-1)/D+(A-1)/((C*D)/mygcd(C,D)))<<endl;
}