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;
#define ll long long
ll a,b,c,d;
ll gcd(ll x,ll y){
    return y==0?x:gcd(y,x%y);
}
int main(){
	cin>>a>>b>>c>>d;
	ll o=c/gcd(c,d)*d;
	ll d1=b/c-(a-1)/c,d2=b/d-(a-1)/d,d3=b/o-(a-1)/o;
	ll all=d1+d2-d3;
	cout<<(b-a+1)-all;
	
}