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;
long long gcd(long long l,long long w){
	if(w==0)return l;
	return gcd(w,l%w);
}
long long a,b,c,d,e,f;
int main(){
	scanf("%lld%lld%lld%lld",&a,&b,&c,&d);
	e=c/gcd(c,d)*d;
	f=b/c+b/d-b/e-(a-1)/c-(a-1)/d+(a-1)/e;
	printf("%lld",b-a+1-f);
}