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>
using namespace std;

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

int main(){
  long long A,B,C,D;
  cin >> A >> B >> C >> D;
  cout <<B-A+1-( B/C - (A-1)/C + B/D - (A-1)/D -B/(C*D/gcd(C,D)) + (A-1)/(C*D/gcd(C,D))) <<endl;
}