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>
long long a,b,c,d,t,g,s;
long long gcd(long long x,long long y)
{
	if(y==0)return x;
	return gcd(y,x%y);
}
int main()
{
	scanf("%lld%lld%lld%lld",&a,&b,&c,&d);
	if(a%c==0||a%d==0)s--;
	s+=b-a+1;
	g=d/gcd(d,c)*c;
	t=b/c-a/c+b/d-a/d;
	t-=(b/g-a/g);
	printf("%lld",s-t);
}
