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;
typedef long long ll;
ll a,b,c,d,f;
ll gcd(ll a,ll b){
    return b?gcd(b,a%b):a;
}
ll fun(ll x,ll y){
    return x/c+x/d-x/y;
}
int main(){
    cin>>a>>b>>c>>d;
    f=gcd(c,d);
    ll p=c*d/f;
    cout<<b-a+1-(fun(b,p)-fun(a-1,p))<<endl;
}
