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;

int gcd(int a, int b){
  return b ? (gcd(b, a%b)): a;
}

int main(){
  long long int a, b, c, d;
  cin >> a >> b >> c >> d;

  a--;
  long long int max_divisor = c * d / gcd(c, d);

  cout << b - a - (b/c + b/d - b/max_divisor - (a/c + a/d - a/max_divisor));
}