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 int ll;
ll GCD(ll x,ll y){if(x%y==0)return y;else return GCD(y,x%y);}
ll LCM(ll x,ll y){return x*y/GCD(x,y);}
int main(){
	ll A,B,C,D,ans;
	cin>>A>>B>>C>>D;A--;
	ans=B-(B/C+B/D-B/LCM(C,D));
	ans-=A-(A/C+A/D-A/LCM(C,D));
	cout<<ans;
	return 0;
}