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>
typedef long long ll;
using namespace std;

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

int main() {
  ll a,b,c,d;
  cin>>a>>b>>c>>d;
  ll n_c=b/c-(a-1)/c;
  ll n_d=b/d-(a-1)/d;
  ll l=c/gcd(c,d)*d;
  ll n_cd=b/l-(a-1)/l;
  cout<<b-a+1-(n_c+n_d-n_cd)<<endl;
  return 0;
}

