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,m,n,tmp,s;
  cin >> A >> B >> C >> D;
  m=C;
  n=D;
  while(m%n!=0){
    tmp=n;
    n=m%n;
    m=tmp;
    }
  m=C*D/n;
  s+=B/C-(A-1)/C;
  s+=B/D-(A-1)/D;
  s-=B/m-(A-1)/m;
  s=B+1-A-s;
  cout << s << endl;
}