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;
long gcd(long c,long d){
  if(c%d==0)return d;
  return gcd(d,c%d);
}
int main(){
  long a,b,c,d;cin>>a>>b>>c>>d;
  long e=c*d/gcd(c,d);
  cout<< (b-a+1)-((b/c-(a-1)/c)+(b/d-(a-1)/d)-(b/e-(a-1)/e));
  
}