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 main(){
  long A,B,C,D;cin>>A>>B>>C>>D;
  
  long P=C,Q=D;
  if(P<Q)swap(P,Q);
  while(P%Q!=0){
    P=P%Q;
    swap(P,Q);
  }
  Q=C*D/Q;
  long a=(A-1)/C,b=B/C,c=(A-1)/D,d=B/D,e=(A-1)/Q,f=B/Q;
  cout<<B-A+1-b+a-d+c+f-e<<endl;
}