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 <cstdio>
#include <iostream>
#include <cmath>
#define ll long long
using namespace std;
ll A,B,C,D;
ll gcd(ll x,ll y){
	if(y==0)return x;
	return gcd(y,x%y);
}
int main(){
	cin>>A>>B>>C>>D;
	ll p=B/C-(A-1)/C+B/D-(A-1)/D,kk=C/gcd(C,D)*D;
	p-=B/kk-(A-1)/kk;
	cout<<(B-A+1-p)<<endl;;
	return 0;
}