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 a,int b){
  if(b==0)return a;
  else return gcd(b,a%b);
}

int main(){
  long long A,B,C,D;
  cin>>A>>B>>C>>D;
  A--;
  long long CD = C*D/gcd(C,D);
  cout << B - B/C - B/D + B/CD - A + A/C + A/D - A/CD << endl;
}