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>
using namespace std;
long long gcd(long long a, long long b)
{
    return b ? gcd(b, a % b) : a;
}
int main(){
  long long a,b,c,d,e;
  cin>>a>>b>>c>>d;
  e = (c * d) /gcd(c,d);
  cout<<(b-a+1) - (b/c) - (b/d) + ((a-1)/c) + ((a-1)/d) + (b/e) - ((a-1)/e) <<endl;
}