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;
using ll = long long;

ll a,b,c,d;

ll gcd(ll x,ll y){
    return y==0 ? x : gcd(y,x%y);
}

ll lcm(ll x,ll y){
    return x/gcd(x,y)*y;
}

ll f(ll x){
    return x/c+x/d-x/lcm(c,d);
}

int main(){
    cin>>a>>b>>c>>d;
    cout<<(b-a+1)-(f(b)-f(a-1))<<endl;
}