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>
#include<stdlib.h>
using namespace std;
int 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=GCD(c,d);
  long long lcm=c*d/e;
  c=b/c-(a-1)/c;
  d=b/d-(a-1)/d;
  e=b/lcm-(a-1)/lcm;
  cout << b-a+1-c-d+e << endl;
}