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 long a, b, c, d, k, l, g;
  cin >> a >> b >> c >> d;
  k=c;
  l=d;
  if(c<d){
    k=d;
    l=c;
  }
  g=l%k;
  while(g!=0){
    l=k;
    k=g;
    g=l%k;
  }
  cout << b-a+1-b/c+(a-1)/c-b/d+(a-1)/d+b/(c/k*d)-(a-1)/(c/k*d) << endl;
}