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;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
ll gcd(ll a,ll b){
  if(!b) return a;
  return gcd(b,a%b);
}
int main(){
    ll a,b,c,d;
    cin>>a>>b>>c>>d;
    cout<<(b-a+1)-(b/c+b/d-b/((c*d)/gcd(c,d))-((a-1)/c+(a-1)/d-(a-1)/((c*d)/gcd(c,d))));
}