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 c,d,g,q;
ll gcd(ll a,ll b){
	if(b==0)return a;
	return gcd(b,a%b);
}
ll f(ll x){
	return x/c+x/d-x/q;
}
int main(){
	ll a,b;cin>>a>>b>>c>>d;
	g=gcd(c,d);
	q=c/g*d;
	cout<<b-a+1-f(b)+f(a-1);
	return 0;
}
