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

}


