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 g(int c,int d){
  if(c>d)
    return g(d,c);
  if(c==0)
    return d;
  return g(d%c,c);
}
int main(){
  int64_t a,b,c,d;
  cin>>a>>b>>c>>d;
  a--;
  int64_t l=c*d/g(c,d);
  cout<<(b-b/c-b/d+b/l)-(a-a/c-a/d+a/l)<<endl;
}