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>
long long gcd(long long m,long long n){
  if (n==0)return m;
  else{
    return gcd(n,m%n);
  }
  return 0;
}
int main(){
  long long a,b,c,d,tmp,g;
  std::cin >> a>>b>>c>>d;
  --a;
  g=c*d/gcd(c,d);
  tmp=b/c+b/d-b/g-a/c-a/d+a/g;
  std::cout << b-a-tmp << '\n';
}
