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 gcd(int x,int y){
  if (y) return gcd(y,x%y);
  else return x;
}

int main(void){
  long long a,b,po=0,c,d,t;
  cin >> a >> b >> c >> d;
  po+=b/c-(a-1)/c;
  po+=b/d-(a-1)/d;
  t=c*d/gcd(c,d);
  po-=b/t-(a-1)/t;
  cout << b-a+1-po << endl;
  return 0;
}