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;
signed gcd(long long x, long long y) {if (y == 0)return x;long long z=gcd(y, x % y);return z;}
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/gcd(c,d)*d)+(a-1)/(c/gcd(c,d)*d))<<endl;
}