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(){
  int64_t a,b,c,d;
  cin >> a >> b >> c >> d;
  int64_t g=max(c,d),l=min(c,d),n=l;
  while(g%l!=0){
    n=g%l;
    g=l;
    l=n;
  }
  n=c*d/n;
  cout << b-a+1-b/c+(a-1)/c-b/d+(a-1)/d+b/n-(a-1)/n << endl;
  return 0;
}