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 long GCD(long long a, long long b){
	if(b==0) return a;
  else return GCD(b,a%b);
}

int main(){
  
  long A,B,C,D,E,aa,bb;
  cin >>A>>B>>C>>D;
  E=C*D/GCD(C,D);
  aa=B/C-(A-1)/C+B/D-(A-1)/D;
  bb=B/E-(A-1)/E;
  
  cout << B-A+1-aa+bb << endl;
  
}