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>
#define LL long long
using namespace std;

LL a,b,c,d,g;

LL gcd(LL a,LL b)
{
	if(!b) return a;
	return gcd(b,a%b);
}

LL get(LL x)
{
	return x-x/c-x/d+x/g;
}

int main()
{
	scanf("%lld%lld%lld%lld",&a,&b,&c,&d);
	g=gcd(c,d);g=c*d/g;
	LL ans=get(b)-get(a-1);
	printf("%lld",ans);
}