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;
typedef long long ll;

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

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

int main(){
    ll a,b,c,d;
    cin>>a>>b>>c>>d;
    cout<<b-b/c-b/d+b/lcm(c,d)-((a-1)-(a-1)/c-(a-1)/d+(a-1)/lcm(c,d))<<endl;
}
